That's like saying if you put a sample image in with a GPL paint program, the sample images gets GPL'd.
The games themselves are not critical to the operation, and any emulator could play them. They are merely *data* that the program acts upon, not the program itself. Sure, with an emulator it can be harder to see the line, but it's still there.
The Linux kernel is GPL but it also has non-GPL firmware binary blobs etc. It's not the same. There's a clear boundary where "the GPL program" and "data that it acts upon" are separated.
A TZX or SNA or Z80 or TAP file that could be replaced with any other in the world doesn't automatically bring that under GPL. And an emulator that can be used with any of those files.
It's like claiming that the licence for the source code for LibreOffice also affects the example Word document bundled with it.
The bundled games do precisely what they always used to without the GPL code. Proven by the fact that there's a trade and entire website in those files on their own before that emulator ever existed (e.g. World of Spectrum, and I have TAP files going to back to the 90's from Gerton Lunter's Z80 and WinZ80).
What you might be thinking of is MAME-style licensing that forbids bundling the games themselves.
The only question mark really is the Spectrum ROMs which are presumably licensed from Sinclair/Amstrad/Sky and ARE necessary to boot the emulator and run any ZX Spectrum game. However, even they can be under any license separate to the GPL because they aren't part of the build process, can be swapped out for alternate ROMs (e.g. Timex Sinclair, Russian clones aplenty, homebrew ROMs etc.), and aren't being distributed as source code.