As someone who's done a couple of safeguarding courses for various jobs:
If I saw a situation like this, I'd speak to a coach, or ideally I'd find out who at the rink was the designated safeguarding lead and speak to them, something along the lines of "I've seen XYZ behaviour from parent X, I'm a little concerned about it, and wanted you to be aware."
After that, you've played your part. Safeguarding is important, and although this kind of interaction may only be a snapshot, it could be a piece in a bigger puzzle. Coaches/rinks can then reach out to other agencies with their concerns and it can progress from there, if necessary.
My thought is, if this is how a parent is treating a child in public, what's going on behind closed doors?
Better to pass on concerns and it be nothing, than stay quiet in my opinion.