What can I do to see this toxic player punished?

Normally I'd say just report them and annotate it in the description, but with the threat of doxxing I'd go ahead and put it in a Support Ticket. Use the category I have a question > Game & Features > General Questions.

You report them and move on. Nobody is obligated to make you feel better.

ok, i have to admit, "skid mark in the underwear of life" made me nearly piss myself.

but all you can do is report and pray others did too, riot wont do ANYTHING (irritating) unless they have multiple reports.

I hope you copy and pasted that chat into your report.