I don't think it's Linux.

I think Tim Sweeney is just like all of the big publicly traded companies where they do not want the best thing for their customers and only want to control them.

Valve, and thus Gabe Newell, is actually making pro-consumer choices, which is success that Tim Sweeney wants.

I think the grudge is against Gabe Newell and Valve.

There is a chance that Tim Sweeney would actively shit on Linux anyway, since that would reduce control over consumers (and yes with all of the deceptive practices Epic does and how they fight lawsuits in court, they definitely are not trying to give control to the users).