Private equity is a type of private ownership, even if it doesn't apply to Steam. In the broader context of business dysfunction, public-vs-private ownership is not telling the full story. Corporate raiding is also just part of the picture; MBA-driven corporate mismanagement, ZIRP and LIRP, principal-agent mismatch, short-term profit maximalism, and a number of other issues are involved too.
A private founder-owner-CEO combination (like Steam) might be the least vulnerable organization to many of those ills, short of a cooperative (not sure it counts as private ownership).