Emulation itself is legal, but downloading and playing game ROMs (the game files) you do not own is not. Most emulation projects, including RPCS3, strongly encourage users to dump their own legally purchased game discs for personal use. The emulation community prides itself on preservation, not piracy. Many emulators also require you to install the official PS3 system firmware, which can be legally downloaded from Sony's website.
Fake sites often embed YouTube gameplay footage into a custom frame to make it look like the game is running inside the browser window. Look closely at input lag and UI elements to spot the trick. The Future: Will We Ever See a Real PS3 Browser Emulator? ps3 emulator on browser