No they do not. REP token holders get a "house take" in some contexts. Augur isn't a company, so a business model doesn't really make sense. Augur is a protocol, and the Forecast Foundation is a non-profit that supports some development.
Who got the $5 million?
The foundation to fund development (which they kept in Ether so is much more valuable than $5million when the sale happened).
He's right, it's a protocol. There is no method for them to take a cut. The protocol gives the fees to the REP holders who report the outcome by staking their REP tokens.
Tl;dr is that 80% went to public, 16% to founders and 4% to foundation.