@m4r35n357 Your thought-provoking answer did help. Yes, my use of "complete" here is not very helpful. A case of thinking out loud perhaps. I had completely failed to notice the "HUD" clock, in the top left corner. I also failed at first to read the info box, or maybe I read only the first part, not realizing I could scroll down to see more.

@m4r35n357 BTW, I edited my question just now so it could be reopened. I also added to the question something that occurred to me while reading your info box, which is that the animation should be running at a normal rate of time flow, where it takes at least year for something to move light year, and that means the twins paradox animation/game or other relativity simulation would need journeys to things merely light seconds or minutes away, and huge accelerations

...to get close to the speed of light in that short distance. Fortunately, it is a misconception that large accelerations means general relativity in needed (that's needed only for large gravitational effects.) so there's no problem there.

@FlatterMann I think a spinning ice skater is an awesome illustration of both conservation of angular momentum and conservation of energy. On its own, seeing a video of such a skater will not make a competent physicist out of someone, but it has its place, I think. Are you saying it's a waste of time to show such vids to students?

@naturallyInconsistent "The difficulty is to make the animation possible for students to understand while at the same time be accurate." That's usually a problem with education and/or popularization of science. "There would be too many things happening on the screen at the same time for students to reliably grasp what is happening." That could be a problem.

But students could watch the video more than once. Also, by having one screen, or video, for each frame of reference, and perhaps also showing only what happens, and not what looks like is happening (blue shifts, rotations and so on) due to tricks of the light, the scenes could be made simpler.

" isolate the accelerating part from the non-accelerating contribution to time dilation." I think acceleration doesn't contribute to time dilation (that's a myth I believed until recently) except by changing the velocity, which is the only thing that directly causes time dilation.