Mobile Gaming Headset I don't think they are anything that could be ONLY for gaming phones. (I actually never heard of that)
Only (wireless) Headset/Headphones to listen the Music and Talk to your Phone (if you have a Microphone) for calling and play the games (if you have on Headseat and go to settings for that). Only this is a point.
Smart Phone isn't made for (only) games. It is made any of this software which is require many things that you can install like in the Computer and go to internet some stuff you can do. (Smart phones are computers actually) And it is a PHONE that you can call it.
The games is just made for fun and there are not really much the greatest to play mini games in there phones. In touchscreen is hard to navigate to play some games too. Depends, which game? Like shooting game, that really won't work any of that and it isn't great to play it on touchscreen. Better play some portable games like Gameboy, NDS, PSP that would be great to navigate and has better games too. (Snake is the greatest to play for old Nokia phones game)
You should look on the Internet and download it stuffs. Just use the internet and look everything that might would help.
http://www.playandroid.com/
http://www.androidgamesroom.com/
http://www.gameloft.com/android-games/