From Webster's 1828 Dictionary: 5. The gaming, two games out of three; or the game that decides the contest; or a contest consisting of three games.

AllWords.com Multi-Lingual Dictionary has 16c as "etymology" of rubber in this sense.

Whoa--totally unhelpful for this question, but still interesting:
http://www.symbols.com/index/wordindex-r.html

Theory: When "Aye, there's the rub" flashed into my head, I had the thought that this means a sticking point--something that's uncomfortable for somebody--which would also be the case for the loser(s) of a deciding game. So maybe it came from that author whom I don't care to mention.