As a PS3 owner I have zero interest in playing PS2 games. If Sony had of made it a PS3, and a 28" 1080p TV then I would say it might be a good deal. People purchase TVs with DVD and Bluray built in all the time. Having an HD media player with blu-ray inside your TV would be great (until it breaks down).
As for the 720p, well this is a PS2 so I doubt they could have squeezed 1080p out of it.
I would like to point out however that it's easiest to tell the difference between 720p and 1080p in video game, not in live video. Video games are made pixel by pixel and it's really easy to tell the difference between low (720p) and high (1080p) res graphics. On this particular unit, it should look pretty good since the PS2 was designed for a normal NTSC TV (480i). However, I don't think any games were made for the PS2 that are much above PAL resolutions (which is slightly better than NTSC). So, the games will end up being "up converted" which will make them look a little blockier than on an NTSC or even a PAL TV.
One more thing is, of course, that since this is a 22" monitor you're not going to be playing from a large distance away like you would on a 32"+ TV, so you would be more likely to spot the difference between 720p and 1080p (ala a computer).
Would I purchase one? No, but I wouldn't purchase a PS2 either.