@atrus, of course this is not justified, in no way I fear

The game is in 1920 x 1080, One scene is 3500 x 1080 and another one currently 5000 x 1080, intended to be about the double in width later, so I thought this might be the problem.
But it really is only about the main character and his animations, I fear.
I use rendered scenes and characters, so I thought it might be good to make the char quite big to have a good quality when she's close to the camera. So I used 1024 x 1024 frames, and with a smooth walking animation including start and stop (which currently are just part of the walking cycle), I have a count of nearly 120 frames per direction. So I guess this is a little bit overkill, although it runs very well on my personal rig

Currently, a one frame standing animation takes 4 MB and a walk cycle 445 MB for each direction...
I think I will try to go down to 512 x 512 at maximum, and I will see what I can do with the walk cycle... I just looked up for fun Daedalics Pillars of the Earth, which needs 512 MB and recommends 1024 MB, so I have some way to go there

I always thought that only the textures currently displayed were part of the VRAM, not all the animations at once

Just for information, if a users graphics card has only, say, 512 MB VRAM, what would happen with the game? Will there be "only" stuttering or might there occur some crashes, if it needs 4000 MB like now? I tested the game on my dad's Notebook, which I doubt has as much VRAM (what I will have to check next time I visit him), and it was working well there, too.