I'd suggest there are no stakes. They're conversational tools, but that's about it.
I think the only real issue is that a lot of people want to claim games with complex, heavy rules systems are "rules-light" in order to convince people it's not going to be an issue to adopt or use them, particularly with new player, and this consistently leads to problems where people do try those games, or invest in them, find they are rules-heavy, and don't really play them, wasting money/time and having generally deleterious effects.
I've almost never seen a rules-light game described as anything else (except maliciously, but that's incredibly rare). Whereas I've seen countless people outright lie about whether games are rules-heavy, especially when talking to new players/DMs. The very fact that they decide to actively lie/deceive suggests that they strongly believe there is a stake. Especially as they almost never try such a line with experience RPGers.
I should add that they generally seem to know they're being deceptive because their reactions to it being suggested they're being deceptive are typically either to admit they were stretching the truth or become very defensive in that sort of "Well technically..." way. I once saw someone basically try to suggest D&D wasn't relatively rules-heavy by talking about Rolemaster for god's sake. (As an aside I'd say 5E was at the shallow end of rules-heavy - it's certainly not light or medium - 4E likewise, 3.XE was unquestionably rules-heavy, as was PF1).
I would agree with anyone saying "rules-medium" isn't very useful. Games are either rules-light, rules-heavy or not really either but I'd strongly suggest the vast majority of games are one or the other (light or heavy). CoC is the only one that immediately springs to mind as being in the middle.