Even saying "I agree" and stopping there on a thread, maybe even "lol" has more meaning than the counting. You are just...counting.
In fact, I've been on another forum before where this became an issue. One person abused it so bad that he gained 3000 posts in one day, and any day now a group of 12 people could come on and do the same thing here taking over every spot in the top posters if they really wanted to. Almost every single one of this guys 3000 posts contained no content and was just spamming random numbers. He then took the lead of the number 3 spot in posts, only behind another forum gamer, who was behind the owner of the forums, and this guy wasn't even nearly done yet, he was just going to get another 3000 the next day (The person with the most posts had about 8000 and was the owner of the year and a half old forums) ...when I look for post counts, you know why I'm looking at them? To see who is active in the community and has a lot to say, but if what they say means absolutely nothing and doesn't even contain any of your personality, anything of the like, possibly even a 1 letter post, then they don't really have a lot to say and aren't "active"...it's just spam. Fun spam, but still spam. (For example, when I say "1" on it's own, I'm not saying it any differently than the last guy. I'm just a robot, no personality, and that's not what I came to the forums to read.) Oh, and I'll say this now - if I did what the guy in my example did, I could easily spend a week here and have the most posts for months to come without posting a single letter, that does not stand for "activity". I would not have been capable of doing this in any other section, but in forum games it'd have been a piece of cake.
Edit: Do you guys think we should have an "accurate number" or a "helpful number"? Even if you refuse to believe posting a single number doesn't count as activity, you should at least know that a lot of people don't care who spams the forum games, as proven by this thread, and it showing who actually posts lots of larger, at least slightly meaningful posts would be what we want.
Likes can be...biased to say the least. If I wanted to, I could ask my friends to just like every single one of my 300+ posts, and for each person who does it, I'd get 300 likes, something next to impossible to achieve in a day without a like for a like thread. Just as the top posters is filled with forum games players now, the top likes received people will also have not gotten there legitimately...more importantly, it's as I said - what I want to know is the top posters, not the most liked people. I want to know who is being a truly active member of the community, not who is liked by a ton of people and "popular". (In fact, making a list of top liked people would encourage people to abuse the like system...and possibly even spam all the other parts of the forum as well as the forum games so they have more posts for their friends to like...it'd make the current problem even worse and cause a new one.)
As Zeno originally suggested, the forum games section should not contribute to post count. The only thing this will harm is dramatically changing the top posters currently up there, and possibly causing a little spam in other sections in an attempt to get a high post count, but those can be easily taken care of, or it can cause people to be more active and interesting in them with real posts instead of numbers...that's about it. Honestly, there is no good reason not to do it. Sure, one could argue that we should do the same for all the "lol" posts and that that's impossible...but that doesn't mean we should make posts still count in the forum games.
TL;DR: Zeno is right. Posts in the forum games shouldn't count - it would almost completely solve this problem, and people can still play their forum games. Honestly, adding likes into the mix will only make things worse than they are right now.