How to deal with petty anger?

When someone is doing something which I find disagreeable, and which negatively impacts me, how should I avoid falling into the trap of being angry at them for "sabotaging" me?

By contemplating what you consider being "me". By learning more about the notion of a "me" in terms of skandha and/or sankhara.

Short version is that we may become angry because we strive for things that others might obstruct. Or we may become angry because we believe certain ideas, motives or ideals are "ours". We falsely identify with concepts, and then get upset when others don't agree or behave like we want them to.

More importantly, how do I avoid seeing it as sabotage, when surely they are doing what they think is right?

Interesting observation. In metta bhavana one is encouraged to remind oneself that others do their best to be happy, just like we do ourselves. Reflecting on other people's motives can foster an understanding of other's perspective. Sometimes that can calm our anger to a certain degree.

And Ven. Bodhi's note: MA: When thoughts of sensual desire arise directed towards living beings, the “other sign” is the meditation on foulness (see MN 10.10); when the thoughts are directed to inanimate things, the “other sign” is attention to impermanence. When thoughts of hate arise directed towards living beings, the “other sign” is the meditation on loving-kindness; when they are directed to inanimate things, the “other sign” is attention to the elements (see MN 10.12). The remedy for thoughts connected with delusion is living under a teacher, studying the Dhamma, inquiring into its meaning, listening to the Dhamma, and inquiring into causes.

https://dhammawheel.com/viewtopic.php?f=13&t=18448&p=259181&hilit

Maybe my giving this answer is cheating -- an easy/facile answer, and not the answer you want -- but maybe it helps to see anger as dependently originated.

I.e. it arises in certain circumstances, because of conditions.

The question is full of first-person narrative -- "I find disagreeable", "negatively impacts me", "my Jungler on League of Legends".

Putting that aside, what are the conditions in which anger arises? What if you identify the condition, what if you alter or remove the condition?

You started to identify a condition -- "my inability to stop getting frustrated with video games" -- so the condition is, "with video games". What if you take the video game away? Why not -- would there still be a craving for video games? So the condition is "with video games, and craving"? Now what's that "craving" for exactly -- what are you craving? Is it worth it, to crave that, if it results in frustration? Can you change your attitude to participate more skilfully, e.g. "I don't mind who loses, I just want to play with my friends" or "I just want to play as well as I can". Or if not -- if you can't (I'm not saying you can't, that's for you to decide) -- perhaps you shouldn't play ... like there is no healthy way to smoke cigarettes, if you want to be healthy you have to stop.

Petty anger is resentment.

From DN33 we are told:

Nine grounds for resentment. Thinking: ‘They did wrong to me,’ you harbor resentment. Thinking: ‘They are doing wrong to me’ … ‘They will do wrong to me’ … ‘They did wrong by someone I love’ … ‘They are doing wrong by someone I love’ … ‘They will do wrong by someone I love’ … ‘They helped someone I dislike’ … ‘They are helping someone I dislike’ … Thinking: ‘They will help someone I dislike,’ you harbor resentment.

Nine methods to get rid of resentment. Thinking: ‘They did wrong to me, but what can I possibly do?’ you get rid of resentment. Thinking: ‘They are doing wrong to me …’ … ‘They will do wrong to me …’ … ‘They did wrong by someone I love …’ … ‘They are doing wrong by someone I love …’ … ‘They will do wrong by someone I love …’ … ‘They helped someone I dislike …’ … ‘They are helping someone I dislike …’ … Thinking: ‘They will help someone I dislike, but what can I possibly do?’ you get rid of resentment.

I can confirm through personal experience that the above does in fact work in everyday life. Memorize and repeat.