Yes, I do indeed know that the expression means "End of the Century" and that it doesn't have really anything at all to do with bicycles or any kind of cycle in the literal sense. This would be what's known as a play on words, or a pun.
As far as the card goes, The Brownies are literally reaching the end of their cycling race. So it's the end of a cycle, if not a century. Although a century is certainly part of a cycle. The card meaning would be, "the cycle that you are currently in is coming to a close."
Is anyone buying this yet?