Not the OP, but FWIW I'm British and we also called it that in the late 80s.

Don't we still call it that now?

Dunno, the people I know only played it in primary school. And I left the country in 2018.

Words can change meaning a lot in a lifetime. Not too long ago, someone here called me out for saying "transvestite", which was a surprise given one of my favourite comedians called themselves an "executive transvestite": https://en.wikipedia.org/wiki/Dress_to_Kill_(Eddie_Izzard)

And my mum, when her Alzheimer's was already bad but not quite bad enough she couldn't live in her own home, referred to the cupboard as a "glory hole" — I'd never been aware of meaning #9 until she used it so, "(Scotland and Northern England) A deep built-in cupboard under the eaves or stairs of a house used for general storage, particularly of unrelated or unwanted items stored in some disorder": https://en.wiktionary.org/wiki/glory_hole

Still, could be worse, as I found out when my grandmother used the word "Irish" in the derogatory sense: https://en.wiktionary.org/wiki/Irish#Adjective

It's telephone now

I'm 34 and I have never heard anyone in the UK refer to this game as "telephone" (although I'm aware that that's what Americans call it.)

Is this what the kids say now? Am I getting old?

As with "Chinese Fire drill" (referring to disorganised and chaotic efforts) the problem is that it's racist. Not like mid-20th century US "People who look different are the enemy" level racist, but it's still objectionable.

So we should avoid doing this, "Telephone" is a perfectly good name for this idea, and it's not racist. There are lots of small changes we can make, which make the world slightly better for everybody.

You've made a gross assumption about the etymology of the term. There are multiple theories about the origin, some of the racist and some of them not.