The moment when the game asks for the current sytem time is what's important and not the time when you start it, since the startup time is not always constant. And it would depend on the millisecond, not the second. If then the RNG causes santa clause hats to appear, it certainly qualifies.

Well, there are plenty of games with random drops, and whether those random drops appear is clearly RNG.

I think you are stretching the intent of the post.

There's really nothing limited about it, but in The Moment of Silence the public time displays in the game are actually showing the time that is read from your computer, so it's attempting to immerse the player deeper into the game world that way.

But I don't think there's anything that changes in the game depending on the time or date, but if someone knows more, I can be wrong about this.

Wingspan patches in/out access to in-game backgrounds based on seasons, or sells a cosmetic DLC to enable them all all the time.

https://www.gog.com/en/game/wingspan_seasonal_decorative_pack

How many of you have heard of Dragon Cave?

It's a free dragon collectables game where you have to catch, breed, and raise dragons.
They have special halloween (which has just finished), christmas, and valentine events, where special dragons are released just for those events. And there's also mini games around those events.

Thank you all, some very interesting tidbits are coming up, just have some patience before I can add them to the list, in the meantime go ahead and post as many such cases as you can think of!

I seem to remember Tales of Maj'Eyal having time-limited special events (themed dungeons or the like). However, I'm not sure if the player had to be online to interact with those.

This one is very questionable as to whether it fits this topic (as I'm not clear whether OP still wants us to mention "events" with online aspects), but last I checked, Talisman: Digital Edition has -- at any given time -- one expansion available to try for free (it rotates through most of the main paid expansions week by week). This feature does require the player to be online to start a new game using the currently-free-to-use expansion, but it doesn't require Galaxy, and any game begun with a given "expansion of the week" can be safely suspended and resumed (at least, a local game can) at any later date without an Internet connection, even after the expansion in question is no longer free to try. You can also play as many games using that expansion as you can make time for during its free period.

Apparently the devs have made the Christmas event permanent, just go into the options and activate it. The Santa outfit can also be worn at any time.

However, I found out that there was also an Halloween event, but apparently it isn't possible to see it anymore unfortunately. It turned you into a kind of Ghost Rider and the crates became pumpkins, a real shame that it's no longer available.

I doubt it, but I'm not going to reinstall Ruiner to find out. According to GOGdb, the game was last updated back in 2019, so nothing changed after I played it.

Dying Light has online events. There was recently one for Halloween.

Starbound

Certain furnitures from a shop in the game's main hub can only be bought in specific, real-world weekdays, but that can be bypassed by leaving the shop (no need to close the game or to leave the hub), then advancing the computer's clock to the weekday you want. Not sure if it works in multiplayer, and you can return to the correct date in your clock after getting the items you want.

While FEZ doesn't have limited time events, it does have events within a Timing Window, of which the most annoying of which is a whole dang week. That's for a puzzle that's for 100% completion.

For optional content, Fez goes one special step further by having players decode binary blinks of a star that you can only see though a correctly oriented telescope.

Star Crawlers has a seasonal events