Apparently these things have a bit of screen lag anyway so playing games is pretty much impossible, irrespective of whether you can actually get them connected. Of course, this is only what I've heard though, I could be wrong.
Stated on Elgato's website. The Eye TV EZ is made where there is minimal lag like less than a second. It is hardly noticeable from what they say. I am thinking of getting one and want to get a second opinion from anyone who has used this to play their console system. Thanks