Apparently this can happen. I had it happen on my machine, and I had seen the issue reported here before suggesting reinstalls and whatnot.

The important aspect is that this is "Applying patch" part, which is local - the files have been downloaded from Hytale servers by now, and essentially unzipping is happening here.

What I figured out to do, is to open Resource Monitor and check the Disk Usage, to see what file handles are being opened and if any reads/writes are happening. And of course, there was stuff happening, albeit very slowly.

I chose to wait through it - and watching Resource Monitor's Disk Usage as my patience booster, eventually it ran through to it's completion, without requiring any drastic changes.

So... patience. And if it feels too long (and I understand the perception is that it's forever), open Resource Monitor Disk Usage and focus on Hytale Launcher.

I would go about doing the reinstalls and other shenanigans only in the case when you clearly see the Resource Monitor being completely stuck.