From what I looked up, "spiel" means a long story or speech, usually used to persuade. A rambling sales pitch would be an example of this. Basically, rhetoric. In a way, I could see that concept being related to "playing a game" (a game of words, playing with minds/emotions, etc.) and the way language tends to evolve, I could totally see how the connection could be made in another language to play and games in general through a shift in use over time. Also, some types of games (such as PnP RPGs) make use of long stories and various forms of persuasion as a gameplay mechanic.
Sorry if I rambled a bit, myself. I've always found linguistics and etymology extremely fascinating.