I don't know if this is the sort of answer you're looking for (or if even all that pleasantly viable with no GPU), ~ almost certainly not what you set out looking for, in fact, but, it's the only answer springing to mind [Edit: Except also flare]:

Pioneer Space Sim

It's open source, actively developed, and lots of opportunity to poke around in. Although not just a game dev engine, still may be a fun educational and productive experience.

An oddball answer for consideration on the side at least. ;)

Godot.

Totally opensource, totally free, 2D and 3D, being actively further developed and refined all the time.

I can develop on Godot on a Steam Deck... theoretically, you should be able to run Godot on another ... non standard pc hardware configuration? Both a Deck and a Snapdragon laptop use shared LPDDR5 RAM, as ... well Valve calls it an APU, Snapdragon calls it an NPU, basically, the CPU and GPU just literally are the same physical chip.

Only downside I can think of is that Godot might not be 'the simplest of simple'.

If you want... even more simple...

... maybe consider LÖVE / LÖVR.

Balatro was made in the 2D only LÖVE, and LÖVR is basically the 3D version of it.

Its all buuilt off of LuaJIT, which means its basically all coded in Lua, a bit simpler and easier to understand than the python-like GDScript of Godot, and that Lua basically just gets automagically converted into C(++?), via the built in LuaJIT compiler.

Uh, tl:dr; LÖVE / LÖVR are probably? the simplest and easiest way to do 2D and 3D as a beginner, Godot is a bit more fleshed out, but also more complicated, both are totally open source and free to use.

+1 on Godot as it provides builds for your CPU (you will have headaches with that)

Other option is pico-8 or some JavaScript library to run in a browser.

Gotod will definitely be a better choice all-together, but I'd also recommend looking into some of the smaller fantasy consoles like TIC-80 (or PICO-8, but that one's not free), if that's something that'd interest you.

It's fun to work with, and it's as lightweight as it can get. It does lock you into a particular style, and you probably don't want to do 3D with it (not that it's impossible, just needlessly hard).

It does have some limitations in place, which might not be for everyone, but the point is to experiment with smaller projects and have fun, with a small set of features. It will definitely teach you a lot, but it might be a little bit harder to get into, compared to other full-featured modern editors like Godot. If that's something you're interested in, I highly recommend it, it's my favorite engine for side projects and game-jams.

Here's how it looks in action:
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The OS will be your limiting factor here. Chromebooks I think lack support from most game engines for development. The industry standard is x64 with Windows.

That said if you can install Windows or preferably Linux you’ll have more options. From a search though. Game maker, and Unity don’t support Arm and Linux, while Unreal Engine 5 and ~~GoDot~~ Godot appear to support it.

Maybe in Windows you can get Gamemaker or Unity to work through compatibility. But honestly ~~GoDot~~ Godot seems to be the safest bet to get it to work.

I would not recommend Godot for a beginner. Not only is it complex to use, it does things very differently from most other game engines, even using its own custom programming language. I don't see a beginner succeeding with Godot. The ideal user for Godot is a realtively experienced Unity or Unreal user who is fed up with their bullshit.

I would recommend Game Maker, Construct, GDevelop, RPG Maker.

Game development involves a lot of different skillsets, and you don't necessarily need to learn everything yourself. That hard part is figuring out which role you want to play in the industry.

The "simplest of the simple" for your case might be developing in Javascript with something like Phaser, ImpactJS, PixiJS or MelonJS; BabylonJS if you want to try 3D. But these are frameworks, not proper engines, so you'll be doing a lot of coding, but at least what you make should run on any browser. One interesting thing to note is that older JS libraries like Impact^[The creator of Impact went on to make Q1K3, a "demake" of Quake in 13kb of javascript, which includes textures. Reading the "post-mortem" is an amazing look into size optimization] or KiwiJS aren't necessarily "worse", their main problem will be lack of support and learning material.

If you don't know programming, or if your skill is too low, take this opportunity to get better at it, learn to transform your idea into logical sequences that the computer understands. Learn programming, rely the least you can on external libraries and frameworks, and the engine and language become the least of your concerns, because you'll have a solid base to use any.

Q1K3

A game in the js13kGames 2021 competition. Play it now, for free!

^js13kGames

The engine doesn't matter too much.

The problems and how you solve them are usually sort of the same, in terms of 2d and 3d. Meaning:

If you're doing a 2d platformer or a 3d platformer, you will still need to thing about colliding with the floor and the solution will be similar too. For art, it's the same. if you start from scratch, learning 2d art and learning 3d art is both new to you. But you will have animations in both and engines usually just use some "playanimation" function. So 2d vs. 3d is completely up to you and what you want to make.

I can recommend pygame and panda3d if you like python. They're not new engines and they're "code only". Other engines give you an editor, but I prefer the "code only" approach, because there are no hidden settings that you have to search for in the GUI, it's just code.

But the other engines like godot and unity have a ton of learning material too, so that's probably easier to get started with.