In contrast to the Mozilla situation, the Clippers' owner is in a different place
1) He has a demonstrated history of actual discriminatory behavior. Indeed, he's settled lawsuits for having black and Hispanic renters evicted from his properties that he owns (Sterling's main income comes in real estate). Eich was to be running a company that had numerous inclusive policies for homosexuals as employees even where the government did not require them.
2) He has a demonstrated history of saying absurdly racist things. Eich did not.
3) Eich gave some money to a political campaign that was at the time marginally popular and remains only marginally unpopular, however morally problematic I find that behavior for the cause it promoted, it is a much smaller gesture on the scales of bigotry. Sterling gave some money to a political campaign (NAACP) in order to cover up the fact that he's a dick essentially.
I don't know how much direct pressure can be placed by the league to remove him, but I do know that if nothing happens and the purported statements are true, the Clippers players (and coach) may play slash and burn to get out of LA quickly and they won't be attracting free agent talent for many years, or may have difficulty even getting a team on the court next year. Sterling has never cared about this futility of his team as long as he made a profit (his team is among the most famously inept in all of sports throughout his tenure as owner), but there are new requirements of minimum salaries that may reduce that ability to keep making money off of a bad team. It may not even be practical and profitable for him to continue to own the team even if the league cannot remove him over these statements and documented history of bigotry.