No. Magic Bitboards are what you use if you don't have PEXT available. EDIT: I expect the WASM version to use magic-bitboards (which is just a "magical" multiply instruction + a lookup).
Every single sliding piece (ie: Rooks, Bishops, and Queens) use PEXT (or magic-bitboards if the PEXT code is unavailable) to determine where to go. Its a fundamental calculation to determine very, very quickly which moves are legal or not.
Both PEXT and Magic Bitboards are incredible techniques for solving the sliding-piece question. However, PEXT is much much much faster, but relies upon an obscure x86-only assembly instruction (that is slower on AMD Zen or Zen2 unfortunately. So you still need to know your hardware details, Intel machines should use the PEXT version).
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Still, even AMD users want the BMI2 version, which has a bunch of bit-operations that can be optimized that are used all the time. (And besides, AMD Zen3 is actually faster on PEXT now, so PEXT is looking good for the future)
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In either case, I have my doubts that the NNUE neural-net runs anywhere near as good on WASM than on the hand-optimized SIMD / AVX kernels that the Stockfish team wrote.
Even if there's some auto-vectorization that WASM can do, its really hard to beat handcrafted assembly / intrinsics (https://github.com/official-stockfish/Stockfish/blob/master/...)