Well the thing is ... yes Valve has shareholding investors.... Only one that matter as far as anyone knows is Gabe Newell. Given it's private corp, they don't have to publicly tell what his exact ownership is and I think it is known it isn't anymore 100% unlike at some point. However all "as far as we know" indications are, Gabe Newell maintains 50%+ controlling shareholding. Rest of the shareholders as people understand are employees and ex employees, who got private shares as part of compensation packages.

We don't have actual look at the books, but Valve people have on multiple occasion said "Valve doesn't have external investors". Given it was public official comments by official people, I would think they wouldn't lie about it. So there is no external VCs or share external investor investors.

Gabe pretty much has probably pretty universal control only limited by business regulation and maybe whatever clauses the corporate charter has. However since he was at one point sole owner, I doubt it contains anything too much curtailing him. Since the way any other people have gotten shares is by Gabe agreeing to give them or sell them to people in the first place.

As far as I understand at no point has Valve been cash strapped such as to need to ask for external investors. Since it is company founded by two early ex-Microsoft people who had made decently money at Microsoft already before Founding Valve. Gabe ended as sole owner as the other founding owner decided to leave the business and Gabe bought him out.