I have one and have tried it with different apps, including this one. It really doesn't work because you are looking at your phone/tablet screen to tap things. At least that's how I play :D When looking at the game on the TV I couldn't get my hands to tap what my brain was seeing on the TV screen, it was all over the place (better have that confirm donut spending thing on) ;) Maybe I'm just not coordinated though :s
If this were like a typical video game and you had a controller to use to tap then you could look up at the TV screen and navigate around your town. I did experience some lag, but that was on a different device from a few years ago. Things could be better now. I'm sure there are games that would work flawlessly with it. It's a cheap buy though, I say go for it and give it a try. Who doesn't like a new toy to play with :)