Interesting question, A game server generally would have a greater minimum specification than a webserver, that being said most shared hosting servers you'll buy into will be a high spec but because of the huge amount of sites hosted on them it's shared out to be a relatively low spec per site if that makes sense.
Another thing to remember that on a shared hosting web server you won't be able to run application that your game server runs on.
I hope that is of some help
Another thing to remember that on a shared hosting web server you won't be able to run application that your game server runs on.
I hope that is of some help