Playstation 2 to HDMI to Thunderbolt

Hello!!

I would like to get my friend a dance mat for his birthday. We both have macbook airs, and I couldn't find a mat that's compatible with macs. Could I get a PS2 to HDMI converter, and then connect that to an HDMI to thunderbolt converter, so I could connect a playstation 2 console to my mac and use the mac as a monitor to play the game on? Would that work?

What other solutions could work?

Thanks!