Okay, I just did a search and came up with something unexpected. I think I know where "Spiel" fits in now.
Quoted from Wikipedia... "With 1,021 exhibitors from 50 nations (in 2016) SPIEL is the worldwide biggest fair for board games."
It's not about the word "spiel", it's referencing a German board game convention. I'd never heard of that, but the reference makes so much more sense now.
(Additionally, I suspect "Glutton Spiel" is also a pun on the "glockenspiel" which is a miniature xylophone. Some of these Sims jokes have so many layers...)
P.S. The third Hunger Games parody is "The Plunder Games".