If they fire you im starting a rebellion! 
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Maybe im wrong but…
Lets use as an example the game i play , Go (weiqi). After the revolution of AlplaGo alot of Open source programs apeared.
And now even on average computers they beat the best players.
Lets get to a certain position. For the A.I. to get to the right move it needs a number of moves to read ahead.
The stronger the hardware the faster it rerads those ramifications that lead to the best move.
Aoe 4 is real time so i asume it needs more resources to read.
AlphaStar (the A.I. for SC2 made by DeepMindf) for example was never made public so we don’t know how much resources it consumes. Maybe with enough training it can run on lower end computers.
But certainly to play at its max power you will need more than the requirements needed to run Aoe4
This is a good read on how AlphaStar was made: AlphaStar: Mastering the real-time strategy game StarCraft II | DeepMind
While you’re correct about general high powered AI, as they generally can only run on supercomputers, programmers have a way of taking the learned behaviors from the supercomputer and compressing them into smaller less resource intensive instruction file for the AI, its gonna be more likely (in my opinion) that the impossible AI will collect and send data to a supercomputer, which would then run simulations, and return general parameters and counters to common strategies it sees humans using.
I’m no AI programmer so I might be completely wrong, or they may have developed a lower resourse requiring AI for the game, but most computers wouldn’t be able to run a self learning AI.
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Depends on AI architecture.
Input can be via API, not interactive input like AlphaStar or OpenAI (which consume a lot of res).
Anyway, SC2API is open (An API for AI for StarCraft II). And there are “competitions” between bots. And there are bots are unbeatable(for most players…) , and they are taught & run by players/enthusiasts.
So, it’s possible to run a good AI bot on user computer. AI can be run on MS servers.
For example some other guys build an AI with DotaAPI: Making a DotA2 Bot Using ML. Problem | by Musashi Schroeder | Medium
So, there are examples.
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I’m also interested in this, I mean what would the hardest aoe4 computers elo be? 750 to 800ish mabye?
An impossible setting would be downright interesting but Id be happy enough to see a setting that can match the average ladder player… I think that’s elo 1000
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An interesting article here about a new AI developed for Gran Turismo 7:
It sounds exactly like the kind of thing people are hoping for in AoE 4.