It's been established in past episodes that the Cybermen can survive in the vacuum of space without breathing. If that's the case and they have no need to breathe, then they have no breathing apparatus to clog with gold or anything else. The Doctor identifies them here a "machine creatures," further confirming the fact they don't breathe.
It's not clear why gold would affect a cybermat, which in all on-screen appearances are simply metal drones. It's stated here that gold works on Cybermen by clogging their breathing apparatus, but cybermats don't breath.
Sarah Jane: The Doctor's going to be worried about us.
Harry: I'm worried about us!
Harry: Tibias, or rather fetlocks, like a cart horse.
Sarah Jane: My ankles aren't thick!
Kevin Stoney, who plays Tyrum, also appeared in Season 6's Cybermen serial The Invasion.
This story establishes that gold dust can suffocate a Cyberman when introduced into its breathing apparatus. This plot point would play a significant role in Season 19's Earthshock, although by Season 25's Silver Nemesis they could be stopped by gold in any form.