what if you bought the domain name way before any type of trademark/brand (in this instance the video game) was created? Do they still have legal rights to go after your domain?
Not usually, no, unless you do something with the domain to infringe on their business. When people register a company in an attempt to steal an older domain through an IP/trademark type case case it's known as reverse hijacking. It usually doesn't work, but every now and then someone gets lucky and is awarded the domain.