Look for quantisation
For the sake of argument, I'll assume The Game uses something like the D&D system of levels, skill points, and d20s. That gives us a pretty interesting lever to get into the rules of the universe.
Does an individual's performance in a certain area scale in an analogue progression, getting slowly better as they practice and improve, or is their performance quantised - average ability suddenly jumping from one level to the next? Do people identified as "Players" suddenly become more effective at certain apparently unrelated tasks immediately after a traumatic experience? Do Players lose skills they don't practice with, or are gains effectively permanent? Do people suffer from decreased effectiveness when they're wounded, or do they operate at full strength until they suffer enough damage to kill them?
Once you have the rules figured out, you can start making predictions. Person A has no attack bonus; his chance of hitting this target, which has an AC of 10, is exactly 50-50. Person B's ability to charm the opposite sex was measured before and after going into combat; their success spiked 25% after combat, suggesting they leveled up and put skills into Seduction.
Essentially, you're looking for digital or quantised effects in situations you would expect to be analogue. Sudden changes instead of steady progression.
Of course, if your players are sufficiently god-like, they may be playing with rules far too complex for mere humans to understand, rules which would effectively mimic analogue change. Which means...
Look for Plots
Does the world appear to run on Narrativium? Even if the players' actions don't produce quantised effects in the universe, they're still going to need compelling storylines to keep people playing.
So find out - do people identified as "Players" keep finding themselves in unusual and challenging situations with a defined plot that they can follow? And, more importantly, does this happen to a statistically significant degree? Are they regularly put in situations where they need to kill large numbers of people single-handed, without apparent remorse?
In Terry Pratchett's Discworld series, there's actually an element that causes storylines to happen - Narrativium. It's the element or property that all things have that tells them what they are, and what they are supposed to be. You can look for a similar element, and demonstrate that it favours some individuals (the Players) over others.