Notably, Terry built his most recent game, Dicey Dungeons, using haxe.

Does Haxe have drawing tools too? I thought it was just a programming environment (very possible I'm wrong though).

Haxe is just a language. However, there are several graphical frameworks that allow for that. Dicey Dungeons (his newest game) is specifically built off the OpenFL framework which tries to replicate the Flash API.

I always used the Flash WYSISWYG editor for the canvas and graphics, so OpenFL isn't a replacement at all in that respect.

You can actually create graphics in the Flash WYSIWYG editor and import them into OpenFL. You won't get the exact same workflow, but it's not completely lacking the visual tooling either.

Same here. I remember implememting the game loop using one or two timeline frames.

OpenFL, a library for Haxe that implements the Flash API, includes a mechanism to import graphics drawn with Flash's original tooling.

If you happen to know, how does haxe compare to Godot? Would you say it's simpler to draw and get a very basic game/prototype up and running?

Haxe is more like a traditional programming language, not an "engine" or whatever is the right term for Godot.

I would call Godot/Unity/GameMaker an engine-IDE.

You can have an engine like Love or pygame where the engine is literally just a shared object or dll and you need to basically supply your own tools for level design, programming, etc.

Engine-IDEs are one-stop-shops with nearly everything you could need built in (level editor, code editor, particle effect sandbox, etc.).

Super easy. Haxe's Flixel is probably one of the most full featured and easy to use 2d engines around.