Integrity unit is purely a term

It's also almost certainly a purely made up term.

Teams that handle this type of activity are more commonly labelled investigation/intelligence units/groups/teams. There's little requirement for euphemism.

Not too sure why compliance has been mentioned, as that doesn't relate to the customer - only the organisation.

There will be a compliance element to this, but only in the sense that the organisation is legally bound by their own terms of practice, to notify and/or act on this type of information when identified. Hence why they employ an investigative element.

It's not simply to protect their profit, but also their legal position.

But this was a discussion about RH, not the company he allegedly made the bet(s) with. So at least in that regard, compliance is somewhat moot.

Additionally, no matter whether it's been called an integrity unit, or an investigations team, they wouldn't have made contact with RH before any relevant authority did. Indeed, contact with RH would be done via that relevant authority.

They most certainly wouldn't have independently contacted the employer of RH about this matter, as that would almost certainly prove illegal.

The only indication to RH anything was wrong, would be due to some kind of hold on his account/the account he was betting from, while the investigation took place.

There's a lot about this story that suggests certain publications have just made stuff up to fill in the blanks.