My opinion:
“ Should people be credited for the use of their stickfigures in an animation or an art piece, and to what extent?”
Yes, I believe in most cases a person should be credited for the stick figure they made. If it’s in a game the end credits or description. If it’s a video then in the description, comments, or if there’s end credits then end credits. Personally I will try and credit everyone who’s figure I use in the future.

“Is the prospect of credit nullified due to the fact alone that said stickfigure was posted to a website where they can be downloaded for free? Where does the line start, if there even is a line?”

Personally, unless the person outright says they don’t need to be credited, it’s generally the right thing to do. I think it’s most important to credit when it comes to someone’s original figure/character. So say they made an OC or made a new type of weapon figure, that’s when it’s most important. If it’s just some random object or a well known character it’s not as important but it’s just a nice thing to do.

Now if the game is for profit, or the video is on a large channel (let’s go with 100k subscribers) then permission should be had from the creator unless out right said. The creator is relying on this persons creation to make a profit so I see it no different then if it was a comic book character or movie character. Of course again, the original creator may say they don’t want credit and/or don’t need any cut of profit, which is also okay.

In the end, I think it’s just best to credit anyone who’s stuff you used assuming your posting it anywhere. And if the figure used is in a creation which profit is involved, then I think it’s a must to ask. I know I wouldn’t want Flame or any other character I’ve made used in a game or large creators video if it’s for profit and they didn’t ask me (assuming Flame isn’t just there for a quick cameo).