When Gabe Newell at some point leaves Valve, the company will change, no matter if it stays private or goes public.

Depends how that happens. Since frankly I think people think "the way Gabe Newell leaves ownership of Valve is by him eventually dying". Since he has never shown any indication to sell. He has offered shares to employees as part of compensation packages, but as I understand even then he has controlling share.

So ofcourse the most simplest way is "Gabe dies and has done no special arrangement"..... shares go to inheritance to his family. So his wife and children. Which might mean nothing changes or everything changes. Maybe he has given private last wishes, maybe not. However they get to decide. They might decide to keep the company as is. Since given they are inheritors of Gabes fortune, not like they would be immediately hurting for cash.

Second option is.... Gabe does actual official arrangements. This isn't unheard of in case of big private family or personal companies or holdings. For example he might put his shares in a foundation or trust with legally binding last wishes unlike non legally binding personal last wishes. Then what happens is whatever the trust charter is. Given example of say some European industrialist foundadtions like Bosch, instructions are left to run the company as commercial business by board of managers to best benefit of the company finances. However the one option the holders don't have is "sell the company", since the shares are hold up in the foundation/trust with instructions "never sell". Company is to be run profitable enterprise as his and best ability of managers and then... the trust gets the profits and uses them for it's purposes. It might be a private family trust, where upon the money is then shared to Gabes descendants, but don't really have say in "we want to cash out, just lump sell our shares". It could also be as in case of Bosch, that it is charitable foundation. After which all of the business profits of the Bosch conglomerate end up financing various charities, foundations, clinics and so on run by the Bosch stifftung.

It will change no doubt, since well Gabe isn't there anymore with his personal personality and well each person has their own personality and influence. However it might not change as much as people think, if say his heirs decide to keep running the company based on same base ethos and principles as Gabe did.

That or everything might change. Two days after he dies, his estate sells Valve to Electronic Arts.