It could be made relative to the time that needs to be spent to complete the game, and maybe a different category for open ended and multiplayer games.
Treating all games equal would be bad design, because "game" is often only the most generic category they share, they're digital experiences and should be treated as such.
Generate a pie chart based on playtimes, and then let the user adjust it to match their subjective experience. Pre-bias the pie slices by multiplying the default percentage cut by their rating of the game if they've given one.
Maybe something more like other content services - ensure there are multiple competitive fixed-rate game services that take risks and auction/bid on getting a specific game for a season at a time. It could include both an upfront payment and a performance payment.
Deduce how important a game is to people by introducing small amounts of artificial delay when playing it. This could be input delay, or maybe the game freezes up for a second every minute, or it takes a bit longer to launch or something.
Measure the dropoff rate. People should be really willing to keep playing great games even when inconvenient, and drop marginally-fun grindy games faster. With a large enough install base, you shouldn't need to degrade anyone's experience very much to get enough data.
This is pretty much how people A/B test for maximum revenue in “free” to play games monetised using micro transactions and other in app purchases.
It’s turned into pure evil there and it’s probably just as likely to spawn pure evil somewhere else.
What would be a good system to determine a fair amount between games when a user is paying a fixed amount per month for all games?
You could ask for ratings (e.g. overall, originality) but these will be a lot more nuanced than time spent. You could ask users what split between games they think is fair (feels like a lot to ask especially if you're playing a lot of games).