Emulators don't rely on a net connection, so what is happening to you is weird. What method did you use to install and setup Yuzu in Game mode?

I don't think there are any limitations regarding running any non-steam binaries while being offline. I didn't have any issues running emulators like that. Maybe you can try opening Yuzu in desktop mode while being offline to see what happens?

I've had this issue (although it's not wifi-related). I have really no idea what it is, but most of the time, just running it multiple times will get it to start up properly. (ie, just spam "launch game") Sometimes a new update breaks something and it happens a lot more often. Try updating yuzu if it suddenly starts happening (it usually updates once a day, so there's almost always a new update)

Another thing is that, if none of that works, it might be Steam Rom Manager. Sometimes it detects a DLC or update file rather than the actual game file, and so the shortcut that gets added into your game mode doesn't actually link to the correct file. It can be helpful to go into properties (press the gear in the game page) and check to make sure the launch options is correct. You'll have to tap the textbook labeled "launch options" and scroll all the way to the right. There, you'll find a file address. Just make sure that the file address is the actual game file, rather than an update or DLC file

So i have never tested it before but your post made me do the test. I was playing on yuzu when i saw it so i closed it, go airplane mode and tried to launch it. I saw the steam loading circle and after a few second, i’m back to game mode screen for yuzu, just like you. Tried to launch it a second time and it worked, launched a rom and it worked.

Just to see if it wasn’t because i was already playing it before, i shutted it down, still in airplane mode. Restarted it and tried again. It worked too.

What is your yuzu version ?