No.
I think you're reading the part where it says that some SURGE traits are 'from' other metatypes, while others are new and weird. Theoretically, a SURGE trait could override or negate a metatrait, but you don't lose your base type by default. In fact, you still count as your base type for all purposes.
The question came up regarding SURGE and *metavariants*, which are basically built using SURGE traits: 'does Nakarti's Shiva Arms stack with SURGE Shiva Arms? (giving *more* than 6)'. The answer is essentially 'no, you already have the identical Trait', but with the specific other point that Shiva Arms doesn't give '+2 arms', so it wouldn't matter anyway.