Why can't they just stop the people on margin from buying gme? That would be reasonable. But if it's your money, I don't see how it's risky for RH.
FINRA arbitration, and the FINRA complaint process, is highly sympathetic to retail clients. When these clients lose money on GME et al, there will almost certainly be a class-action lawsuit for some fraction of their collective losses. And Robinhood's lawyers will almost certainly recommend they settle. That is the risk, beyond margin lending and options settlement, they are seeking to mitigate.
(Also, when that money is lost, there is a decent chance Robinhood will be fined by half the regulators on this planet for inducing people to overtrade through its gameified interface or something like that.)
If their customers - the firms that pay them, not app users - see the RH platform as a threat to their business they could pull the plug[0]. Or if this prompts regulators to examine RH and similar products.
The risk isn't in the outcomes of options/trades; its risk to their business model.
[0] RH's customer are actually market makers, who by and large will be profiting heavily off of this.
This point has been made repeatedly elsewhere but it bears repeating. Market makers are getting rich off this trading. Robinhood's customers are not hurting from this.
Still, as far as risk to RH is concerned - if this kicks off a change via their customers, regulators, or legal action the change is probably not in their favor.
On one hand, you could say RH shouldn't let people buy options if RH doesn't believe those people can pay up when the option expires. On the other hand, you have people buying options who maybe don't understand that you need cash to buy the shares if the option expires in the money.