That's where the Confusion lies. The quote you show is entirely accurate but is talking about Multiple Attacks into One target which it seems a lot of people have taken to mean you cannot attack Multiple Targets without Multiple Guns. It's that last assumption that is wrong as with the various Bursts and Full Auto attack you can use the Multiple Attacks free Action to spread that burst of full auto across several different targets. What it fails to address is how many targets that can be and what the penalties they take are although prevailing logic consensus seems to reach back to the SR3 (i don't know how it was for SR4) and divides those bursts or FA down to give the equivalent penalty to the targets based on what portion of the attack they are catching.

To see the book for this reference the Long Burst Action under the actions list and later the Full Auto and Burst paragraphs of the Firearms section (pg178). The Multiple Attacks box itself is less descriptively helpful on Page 196 but it gives the mechanics.

So, for examples.

RazorGuy is fighting in close combat with a pair of gangers who decided attacking the samurai while he was alone was a great idea. Razorguy is moderately badass with his Melee of 6 Agility of 6 and a katana (because yes). As per the Multiattack Free action he can make up to 3 attacks in melee with his katana and if he does so it'll be 4 dice each way. Or he can go for 2 attacks at 6 each or 1 attack at 12. These attacks he can divvy up however he chooses. If he's using two melee weapons then things may also work out differently....

Now a little while later on a run Razorguy is confronted by a pair of security guards with lethal intent. He's carrying Twin Uzi's and here he has a few options. 1) He can fire both Uzi's into One Guard using a Simple OR Complex FA Action and a Multiattack free action. 2) He can fire One Uzi into Each Guard with the same actions above. 3) He can fire just One Uzi and walk fire across both guards using the same actions above 4) He can walk fire from Both Uzi's across Both guards.

Where the book sadly fails again in how that is done. But with a little reading between the lines this is how I have interpreted it for my table. (This is not strictly RAW but what i feel is perhaps RAI).

With any One weapon the attack breaks down just as in the first example as as reads fine on pg196.
With two weapons what you get is Two Dice pools, literally multiple attacks (otherwise why ever use two melee weapons? Even if you;re ambidex there's no advantage).
So for Razorguy, if he had 2 Knives instead of a Katana he'd get to make one attack at 12 dice Dexter and 10 Dice sinister OR 6 & 6 Dexter and 10 Sinister OR 12 Dexter and 5 & 5 Sinister.

In the next example (assuming Pool of 12 again with a Smartlink that works for +2 dice) we shall assume that as a runner with some time to have decent skills and abilities he;s probably Gas vented the Uzis. So we shall start with a base recoil of 10 for each gun (full auto complex) his Str (5) gives him 2pts of comp, the Vents 2 points of comp and the base of 1 everyone gets (5). Final of -5 to the Dice pool with with his Dexter is (12+2-5=9) and Sinister (2 less offhand for 7). So he can pump out a FA (Complex) Shot into each guard (@9 and 7 dice respectively) OR he can Pump both into one guard. However he could also Walk Fire across BOTH guards (5 Dice 4 dice Dexter and 4 dice 3 dice Sinister).

If instead he just had an Assault Rifle or just the 1 Uzi or whatever then he could either pump one full burst into one guard or walk fire. But he could NOT split the burst down to target one guard multiple times.

As for the penalties I go with the "Not Enough Bullets" ruling so 10 bullets at a guard is the full -9 penalty to defense, walking fire between the 2 (5 bullets each way) is just -4 to defense vs each hand.

YMMV

Pg.196, under multiple attacks, the third paragraph states" The total number of attacks you can make in a single Action Phase is limited to one-half the attacker’s Combat Skill."

Indeed, for some reason mentally I'd only applied that to Melee combat.

And if RazorGuy at some point in time gets his skill to 12 and his Ag still 6 and will start shooting a swarm of giant bugs with Full Auto from one weapon - he will be able to shoot just 6 of them, each will get -9 to defence, right? So he will split like 3-3-3-3-3-3?
I'm really bad with numbers))

6 targets at 3 dice each (assuming no other mods) is correct with Agl 6 Automatics 12. How you do the defence penalty is upto discussion still. I go for "not enough bullets" rule assuming an even spread between targets (or even letting the player call how much of his Long Burst or FullAuto complex he's pumping into any one target) so the base mid for each would be -9 but if the spray is even then it's 2bullets to 4 targets and 1 bullet to each of the last 2 targets. Using not enough bullets makes the mods -1/-1/-1/-1/0/0 to defence across the targets. Others just reduce the attacks to burst penalties (which, without book to hand becomes 4 x-2 and 2x -1 I think). This is because it's easier to get out of the way of part of the spray than being under the full focus of a Complex Action Full Auto barrage.

There is also some discussion over where to allow the walking fire. I think i lean towards allowing it for any of the bursts (SA/BF short burst or Long Burst, FA simple or complex) with allowing, alongside the 1/2 skill restriction, a maximum number of targets at 1 bullet fired per target (that's why I use not enough bullets for modding the defence rolls). So no matter how good you are you cannot shoot Six targets with a SA triple tap burst.

Again, all this is just how I interpret the Rulesystem as a GM at my table and sone of the logic is taken from my SR3 experiences. Bt it seems to work.

sounds legit

There's no way they should still get the -9 penalty. There should be a trade off: More targets for less effectiveness on each target. Yes, you're only rolling 3 dice but you only need one success and more than likely they wouldn't get to roll any defence dice. The penalty represents the amount of bullets aimed directly at them. If it's one each then there's no penalty. I think the 4th Ed rules for this should largely still apply.

Again, I'm not sure why one interpretation so obviously trumps another. The multi-attack section doesn't mention targets at all except in the example where Wombat (I think?) attacks 2 targets in melee.

I just can't get past the fact that the main intent of the rules changes in SR5 was to streamline combat. This is why you generally can only make one attack in a round now instead of 2. Why would they then intentionally then intend for you to be able to choose to then make complex multi-attacks that bog everything down?

If we're going to really look to the margins with interpretations I could quite easily extrapolate that the quote from page 196 is implying that if you are attempting to multi-attack with 2 SA Pistols then you can fire each as a SA burst.

EDIT: Having re-read the firearm attack mode section the entry under the SA Burst section could quite easily have been added by mistake as it is exacly the same for the Burst and full auto entries. The whole thing though is pretty messy and I agree that you should probably be able to attack multiple enemies with burstfire from automatic weapons. I had assumed that the rules would work in a similar way to how they did in 4th ed where you essentially made 1 roll and just divided your FA burst into smaller bursts with penalties based on the number of targets.

I think that in many cases you'll see fire getting walked by one gun across a pair of targets or twinned guns across a pair of targets to maximise lethality. So sure you've got 2-4 rolls (depending on how you do it, skill levels etc) to hit and similar for dodge and soak, but quite possibley not as often as you'll have people focussing fire because Recoil + Splitting dice pools hurts. On average I doubt combat will be greatly effected by this (except the targets of said attacks may fall over quicker).