I don't know if game shows will be affected by an IATSE Strike. I did see the union's logo online (it resembles a non-pointed star), and to the best of my knowledge I never saw such logo during the closing credits to Price or any game show for that matter (unless something's changed), and I definitely never saw such logo on the closing credits to the 1980s episodes that are presently offered by Pluto. I'd probably see such logo in the closing credits to films, sitcoms, daytime soaps, and prime time dramas, if anything.
That said, I think game shows will likely not be affected. If anything, the strike may affect game shows in a good way - there may end up being an increased number of prime time episodes, just like there was with the WGA strike back in 2007-08.
Or, if a strike impacts programming, they may use "scabs" (replacement workers) to do the work normally done by unions, because the networks need the money.