Adding suffix to your domain (example: Forum) will certainly boost your rankings in search engines for that the keyword forum up to a certain extent. Bing give more weight-age to keyword in a domain than Google does, but yes, google too boost your ranks upwards if some user searches any keyword/group of keywords + forum in their search query.
Secondly, "forum" is descriptive word itself, and so will attract many users who are really searching for your game AND forum. So here the domain exampleForum.com WINS.
But there is also a drawback, if your forum gains immense popularity and one day you want to re-consider the topic of the site from shifting to "Informative site, or eCommerce site" selling that particular game, then the "forum" suffix will do more harm than good. Here instead of forum you can you suffix as +game in the domain name. Example: pubgForum.com vs pubgGame.com , the game has more potential of reach-out among the masses as it is not restricted to the "forum" target.
So its also depends on your current and future usage of the said domain name.