Interesting to think about, certainly.
As far as I am aware, the method for "rating" games on itch is exactly what you've already seen, a bit of an out-of-the-way / almost hidden page where one can write a short review and give out some stars. The problem with this, aside from the fact that it's not really "critique" in any traditional sense, is that itch.io's discoverability is already garbage, and the algorithm is apparently very brutal and devoid of nuance (likely as a result of itch being a fairly small, low budget platform that can't afford to cultivate a powerhouse algorithm) such that if any game gets even one rating below five stars, it's visibility may suffer disproportionally. Of course, this may be mere rumor, but it's said that even a single four star review has been known to hide already difficult to discover games in some nether-region of the search results.
Either way, just in case, it has been somewhat accepted practice amongst the indie developer communities and scenes in my neck of the woods (most I know are based in anglophone countries, with highest concentration in the US) not to leave ratings below five starts on any indie project on principle, so as to avoid actually harming the designer based on something as subjective as opinion based evaluations. Potentially, it can work the other way around, where giving out five star reviews on principle can be seen as a way to show support and solidarity and potentially improve search results. But as is the case with most algorithm based systems, the actual efficacy or veracity of any of the above is hard to verify.
Of course, this then circles us around to the fact that these ratings systems do not actually constitute "critique." As an alumnus of a semi-traditional fine arts college, I am fairly familiar with the concept and process of peer critique, both in terms of taking critique gracefully and dishing it out constructively, and for me it always comes down to two questions.
First, is the critique genuinely constructive (can it be practically applied, is it relevant, does it actively take the role of the personal preferences, opinions, and biases of the critic into rigorous consideration)? If not, then it's not worth engaging in - while we are dealing with art here, it is also art that doubles for many as a commercial product and a source of income, and that may come with limitations. For example, if a game has already been fully published and released and its designer has already moved on to other things, then peer critique isn't applicable or relevant. The thing is what it is. Sure it can be revised (if the release is digital only), but only if the designer is open to that and capable of devoting time to that from a practical perspective. Similarly, if the critique addresses something that is outside of the designer's practical or logistical capabilities (such as the inclusion of artwork that they simply don't have a budget to commission), I again would general refrain.
The second question, when it comes to peer critique, is much more important to me. Has the critique been invited or solicited? If not, then I usually find it rude to give out without asking. This happens way too often in art scenes when certain members become a bit overzealous and overenthusiastic. Back in college, I was home for the summer once and had a friend over who was also an artist, and a student at a different school. She spotted a painting I had done that year just sitting on the floor, and began to give me all sorts of unsolicited advice and criticism, without any prompting or discussion. She didn't even bother to first acknowledge that it was there, ask about it, or ask whether I wanted to talk about it. She just started going off about how I should consider using a more neutral color alongside the flesh tone there, and how she didn't find the perspective convincing, and blah blah. And look, I was in school too, and I had already had that painting critiqued by professors and even a famous visiting painter or two, all of whom gave contradictory crits, and I was tired of it and it was finished, as far as I was concerned, and I was on summer vacation, happy enough to just do art for my own enjoyment for a few months. It was just plain rude. If she had asked, that would be a different story, of course.
But all of that applies specifically to peer critique. When it comes to press critique, that's ultimately a field that, for better or worse, exists on a separate plane from the actual creators, though there is overlap between the participants. In games, both analog and digital, our biggest problem right now is the fact that there simply is no reliable outlet for thoughtful and useful criticism, as most writing about games is dominated by the Enthusiast Press, which is half content-mill and half marketing arm for the bigger corporate players. That isn't to say that thoughtful, qualitative pieces aren't being written, but that they aren't really the norm. When it comes to tabletop, I can't really think of where to even look for some of this sort of work. It's much easier to find quantitative "reviews" of any given thing, again going back to star ratings and grades that attempt to quantify subjective concerns and don't amount to substantive critique.
Of course, there is then also the question of how one does this in the tabletop medium, since it is largely concerned with the building of frameworks for the players to tell their own stories with and is ultimately and extremely odd blend of creative writing, technical writing, pedagogy, and systems design. But if I were to start musing on that I'd be here all day.
So yeah, honestly, problematic indeed. Ultimately, I am not really one who concerns themself with criticism and critique all that much, but I do understand that having centralized outlets for such things can definitely have positive effects on the ecosystem of a creative scene, whether I personally choose to engage with that or not. I imagine at this point, if we actually found a healthy, primarily positive, and nuanced way to talk about an extremely interpretive and multifarious medium, an outlet that wrote about indie games as a sort of "art criticism" could be well appreciated.