I donot think its good to add one. The reason is that people would continue using one-word posts throughout your forum when you encourage it in one particular forum or part of your forum. Besides, since your forum hasnt grown considerably, you are not in a position to warn your members for short posts and it would be very detrimental if you do so.
Ofcourse, you can do it once the forum growth is considerably steady 😉
I never really liked them much so when I first started my forum I didn't add a section for them. Eventually members starting posting a few and they actually seemed to enjoy it so when the main general area became a bit cluttered with them I made a section for it finally.
I think some are amusing, and others though simple/one liners/one word actually help to get to know other members a bit. I just have a rule against counting games (count by 2's, count to infinity, count to x before x, etc) or ones that are too spammy because I find those to be very pointless For example some I've closed are the "CTRL+V" game and "Last Post Wins".
First off, you must consider what, exactly, initially brought those members to your forum -- did they come to engage in quality discussions relating to its niche, or do people go and "talk about anything"?
If the latter, then whether or not you throw forum games won't affect much of the outcome. I just don't think that they really should have any importance.
On my general chat forum, we had a forum games section which was fun for awhile. After some time, that's the only place that was getting new posts. It was very discouraging. I don't know if these type of games work very well if you want new posts in all other subforums but they can be a nice diversion.
if your forum is of a decent size and reasonably active, then go for it. Just turn off post count though. It's nice to play a little range of games to ease your mind off things. Most forums have them nowadays, tbh.