I am making a game, and I have a worries is it legal to use the Trademark Symbol in the logo of the game?
The ™ symbol, is similar to the (c) symbol. There are both used to assert trademarks and copyright respectively. ™ is for unregistered trademarks, while (r) is.
As Dale points out, it's illegal to assert or use a trademark that isn't yours, as it is false and misleading. Using a trademark that is not yours is known as brand piracy.
If you have registered the logo as a trade mark, yes. If not, it is a false and misleading representation (aka a lie) and is illegal in most jurisdictions.