My top line thought is the same as @slugzuki’s - the thing that I’ve most enjoyed in reviews of my games is seeing the reviewer identify and engage with what the game’s trying to do, and analyze how the implementation does or doesn’t support those aims.
The piece I’d add is that specificity is really really helpful - hearing “the game was boring” isn’t that helpful; “the prose was hard to get through” is more useful; “the author has adjectivitis and every sentence has multiple dependent clauses” is gold. This extends to typos, bugs, and puzzle design, so it’s really nice when a reviewer saves a transcript with comments or flags when something either works or doesn’t work (this is expecting a lot from a reviewer, and is only really viable for certain parser systems so it’s definitely not an expectation - but it is useful!)
I will say that the sort of critical essay approach you mention doesn’t seem to me like it’d be as useful to a particular author - and a one-off review might not be the best venue for that kind of analysis since often synthesizing trends or contrasting approaches across different games is going to be more interesting. But value to author isn’t the only criterion to what makes a good review, and there currently isn’t an obvious high-profile vehicle for that kind of criticism in the community. As a reader of reviews, my favorites are the ones where the reviewer found the game sparked something for them - an emotional response, an idea, a connection with some other piece of media - and is excited to share that. So if you’re feeling that spark, I wouldn’t shy away from it!
Finally, there’ve been a couple threads on what makes a good review that might be worth checking out:
https://intfiction.org/t/if-you-want-to-write-reviews-but-dont-know-what-to-write/
https://intfiction.org/t/how-can-i-write-better-reviews-of-comp-entries/
EDIT: also occurred to me that some examples might be helpful? I’ve found Mike Spivey’s reviews of my games very useful, with the fact that he liked my first more than the second not having much impact on how much I got out of reading his thoughts: