I found a site with classic Nintendo and Sega games as they where made in the late 80’s early 90’s for game consoles as NES, SNES and MegaDrive.
There are many other sites with ROMS. You’ll have to download them and then play them with an so called Emulator, freeware software emulating a console. On Every Video Game you don’t have to. You’ll only need a Java capable browser.
The site has NES, Gameboy and Sega Master System versions of Aladdin. The Master System version is different then the other versions I know.
It’s a race against time and seems to be inspired by the Amiga game Prince of Persia. Jasmine plays a larger role here, while you can’t control her directly she follows Aladdin while trying to escape the guards.