You can play PS2 games without the need for the console as long as you have a PS2 BIOS.
Also, without this BIOS, you cannot run PS2 games on your Android phone. Using a PS2 emulator for Android phones is fairly straightforward. This may be one of the Frequently Asked Questions (FAQs) related to PS2 emulators nowadays. Technically, any types of emulators are considered legitimate. What it does is simply imitating the hardware of gaming consoles then turn it into a software.
