I'm not a Valve employee but I can imagine a rolling update would not be easy considering all these games are constantly connected to the various game servers. They would reconnect immediatelly upon losing the connection and could reach an existing game server running the old software version. Then the rolling upgrade reaches that game server and once again the user is disconnected. And so on.

Blue/green deployments would be better but I'm guessing the scale at which they operate is massive. Back in the old days I managed a fleet of Counter-Strike servers and they were super heavy on CPU/network. Spinning up a complete infrastructure to switch all gamers at once would be too costly, even for Valve.

I doubt anyone at Valve will be at liberty of discussing the specifics you're asking about, so these are my $0.02

Because Valve doesn't have an insane amount of employees and since it is not critical software, the downtime is fine.

The very existence of this thread proves that it's not fine.

I think it depends on your definition of “fine.” No one will die or even be particularly inconvenienced from not being able to play a particular game for a couple of hours at the same time every week. Steam alone has hundreds of thousands of other games that ARE available at that time.

I don't know for sure, but I'd speculate that it is more about customer service than technical capability. While it seems like a bad experience to expect downtime every week, it would be worse to be told "No more Tuesday maintenance!", and then have it end up happening anyway because something went wrong. And things do go wrong in this industry. Leaving the maintenance window open gives them more flexibility to get a variety of work done without having to worry about ticking off the gamers because of changing expectations.

Obviously we know what you mean and this is a bit of pedantry, but I think blue-green deployment is the term to use.

Because the janitor keeps plugging the server out to plug in his vacuum.

Unrelated, but another company that used to (still does?) the same thing was Konami with PES from 2017-2020.

Because is cheaper