I think by trying to decide the rubric you'll use, you're focusing on one of the least important parts of writing a good review. I think the most important thing to remember is that a review is a type of persuasive essay. Instead of thinking about what elements you'll rate and how, you'd be wise to be thinking about what goes into building a strong argument.
There are a couple things at play that make picking out a strong rubric an unnecessary task. One is that every game is very different. What kind of rubric could possibly fairly review a walking simulator like The Stanely Parable, a high-action game like Devil May Cry, a sandbox like Minecraft, and an online experience like Fornite? They all have very different goals and need to be considered on their own merits.
But far more importantly, people won't be reading your reviews because they want a scientifically precise score. They'll be reading them because they want to decide whether a game is worth playing. A rubric is a tool that can be used to this end, but it's not the end goal in itself. The end goal is for you to indicate whether you think a game lives up to its promises and why.
The way you accomplish this is with a well-argued explanation of your opinion. The key word is "well-argued."
A strong persuasive essay uses one technique very heavily: It backs up all of its claims using specific evidence. You could use a rburic to say, for example, that a game's story is a 4 out of 5. But why do you think that is? What specifically about the story makes it good, but not perfect?
For example, I'd say I rate the story of The Legend of Zelda: The Twilight Princess a 4 out of 5. The game has a whole cast of side characters who go on surprisingly deep arcs. But the story has some missteps that keep it from being perfect.
(Notice that at this point in my review, it's going to be very easy to dismiss my opinion of the story. Perhaps you love Midna's character development and think the story is the strongest in the Zelda franchise. Maybe you think the game is overly dark, to the point that it's just silly. But I haven't given you anything to argue with, so the score I offered only serves to tell you what I think. And if you were considering buying Twilight Princess without knowing much about the game, this opinion doesn't help you decide whether you'll end up enjoying the story for yourself.)
What I like about Twilight Princess's story is that so many of the characters are surprisingly well-written. At the beginning of the game, a group of children are kidnapped by monsters. After you rescue them, they continue to show up throughout the story, and each one ends up having their own side story that lasts the entirety of the game. One timid boy learns to find his courage by following Link's example, and a different bratty girl finds herself helping other people and becomes kindhearted. Most dungeons are more than just looking for a mcguffin in an abandoned temple. Instead, they are tied to side characters dealing with heavy problems. One particularly memorable level is a mansion lived in by a friendly yeti and his sick wife. Not only are you looking for the mcguffin Link needs for his quest, you're searching for a cure for this sweet lady. The warmth the couple offer you when you interact with them contrasts surreally with how empty, inhospitable, and monster-filled the rest of the mansion is, hinting that something is wrong. When the pieces all come together, you're treated to a particularly emotional boss fight, and what happens to the wife hints at how pwoerful the mcguffins truly are, tying this couple's side story into the game's broader narrative.
And of course, you can't talk about Twilight Princess's character arcs without talking about Midna. Link's companion in this game is a strange imp who starts out openly emotionally manipulating Link to further her own agenda. She clearly does not care about anyone besides herself. But as you adventure with her, the consequences of her selfishness catch up with her and makes the very problems she was running from far worse. In order to complete her goals and help Link save the day, she finds herself caring, whether she wants to or not.
The story has one particularly large problem, unfortunately. It starts out with a new Zelda villain, the dark sorcerer Zant, who effortlessly conquers Hyrule before the story even opens. He's presented as frighteningly competent, and a Zelda game exploring a new villain is exciting. But halfway through the game, without any foreshadowing, it's revealed that he's merely the puppet of another big bad, someone very safe and familiar for Nintendo. It's disappointing that Nintendo would throw out such an interesting plot point, especially since it's handled ungracefully.
Now at this point in my review, I've cited several pieces of specific moments from Twilight Princess. I reference multiple side characters and describe one of the dungeons in detail, pulling out story beats that support my claim that the story is written strongly. And I focus very clearly on Zant being overshadowed by Ganon as the reason I think the story could be stronger. You can still disagree with my 4 out of 5 score, but now you know why my view is the way it is. And if you're considering buying the game, you know to expect a lot of cool side stories but not to be too surprised when the main story is a little sloppy. This lets you consider what you think it important in a game's story and form your own decision about whether the game is worth your money.
You should strive to write your reviews like this. You can use pretty much whatever rubric you find helpful. You can omit a rubric altogether if you want! But make sure that all of your opinions are backed up by specific references to the game being reviewed. This both makes your opinions stronger and gives readers considering which games to buy the context they need to make informed decisions.
