Personally, I think we all play games. We don't have a choice; no one always says what they mean, or even knows what they mean or want. Some of us play games more deliberately than others, of course.
According to my experience, what you describe, Chewy, is not uncommon: one or both partners often "re-engage" (it doesn't seem to matter who was the relationship "breaker," either party may initiate). The easiest examples for me are from college, where it was easy to observe a lot of fairly committed relationships from close range (due to enforced proximity of school). One of my roommates broke up with his girlfriend of 6-8 months, and for a month or two afterwards, they would periodically end up in each others' beds. I saw the same kind of pattern with several couples.
The one time my girlfriend and I broke up (she later became my wife), we sort of got back together once after about a week or so. However, we didn't speak after that (for a mostly unrelated reason) for a few months. I don't even remember how we got back together...it was sort of a gradual thing....
Anyway, both of us played many games...our relationship has been a struggle for understanding (and the invalidation that comes from not understanding) and, at times, will. I don't think any of this is abnormal; we love each other very much, but communication is difficult, so we have some struggles.