An anti-SLAPP law usually works by giving you a special motion that lets you say "hey, I think this is a SLAPP lawsuit", which basically gives you access to fee shifting (making the loser pay the winner's legal fees). Copyright already has this built in.
Which is great news... for Nintendo.
The problem that Nintendo is citing in their lawsuit is the fact that Yuzu ships Switch common keys. For the purpose of DMCA 1201, this is a smoking gun[0]. There isn't really a good legal argument for why emulators should be allowed to ship decryption keys, or at least, the EFF refused to come up with one when Dolphin asked for legal advice on this point a while ago. So if you go to court and provide a completely legally baseless argument, Nintendo wins, and then they move for fee shifting, which means they get to prosecute the case for free[1].
[0] While it is true that the scope of DMCA 1201 is far wider than just encryption keys, in this case, Nintendo has only cited the keys being in the emulator and the fact that Yuzu is really useful for running pirated software, which is "good enough".
[1] In practice, it's more "for cheap" than "for free", because there's specific rules about how much you're allowed to fee shift, a whole bunch of stuff about 'lodestar amounts', etc.