One, Two Worlds II is listed under Action and RPG. The product in the store is named "Two Worlds 2: Epic Edition". If you don't see it, ensure you don't have an addon hiding owned games enabled. The games in the library are named "Two Worlds II Velvet Edition" and "Two Worlds II Castle Defense".

Two, I don't see any patch download links either in the base game or the expansion. Download the game, install and play it.

edit edit:
Mouse over the English installer download. It links to "gogdownloader://two_worlds_ii_velvet_edition/installer_win_en" -- this is a downloader link.
Now mouse over the "blah blah patch" (or try clicking it, or whatever). Nothing happens, because it's not a link, it's a leftover text heading from before the patches were incorporated into the installer and removed.

It's actually quite simple.

Both installers and patches have version numbers (as part of the file name and/or displayed in the download window). Barring GOG bugs, if the patch's version number is higher than the installer's, you do need to apply the patch after installing the installer; if the patch's version number is lower than or equal to the installer's, you need not. Both cases regularly occur in one's library.

That said, I believe there's no harm in always attempting to apply the patch, as, barring GOG bugs, the patch usually checks whether it can be applied prior to running.

P.S. The attached image you posted has no patch. What you circled is a header with nothing under it.

From what I've been able to tell from following Outcast 1.1 and Witcher 2/3, the patches disappear once the game download has been updated to include them, so it'd be safe to assume that patches being available for a game means that the game download itself isn't fully updated yet. Like right now the base Witcher 3 game is 1.06, and there's a patch to update it to the latest version, 1.10.

But if the links aren't there, then the game download should be updated to the latest version (and that patch section will still be there, only minus links, which can be a bit confusing).

One. Two Worlds II doesn't show up on my library whenever I select ANY genre. I wasn't talking about the store page, I was talking about the Account page that lists all of our games. No matter which genre I select, Two Worlds II doesn't show up. Two Worlds (one) shows up when I select "Action" but not "Role Playing" and Two Worlds Castle Defense shows up when I select "Strategy" but Two Worlds II doesn't show up for any genre.

Two: No, there is no patch available for download (at the moment) for Two Worlds II. I wasn't talking specifically about that. It's just that tonight I was downloading Two Worlds II and it reminded me once again of how when there is a patch listed there, it's not always clear to me whether or not we're supposed to download both.

Oh you can friend request him but not me?! Think of all the movie references we had together? Do they mean nothing to you?! =p

You're already on the my list fart knocker! :P

I wouldn't worry about it -- the dumbest question is the one you never ask when you're ignorant of a certain fact.

It never hurts to ask for advice if you don't know something!

Am I missing something then? (See screenshot to this post)

Again, I know Two Worlds II doesn't have a patch at the moment, that just happened to be the game I was downloading tonight when I saw the listing there and it reminded me of the nagging question. But I am not seeing any version numbers on the game in this screenshot that does have a patch(s) listed or I'm missing something.

Ohhh.... Well then... This is awkward and comes as a surprise....
Didn't know you accepted my request... So you accepted? So this means your MY innkeeper now! And I'm YOUR janitor! (Love is in the air starts to play) =p

I don't care how stupid the question is, I have it beat in both level and number! :P

Believe it depends on the game. Older installers lack the (GOG-x) bit.

Really? That's stupid, it's not very customer friendly.

Do you have a rough idea, given your vast store of data, how often gog's version numbers are bugged? I dl'd my record number of accumulated updates recently and found myself wondering this often.

(Off the computer right... now. Thanks in advance & have a nice weekend.)

GOG has clearly stated that they are no longer supporting the downloader. They seem to believe that galaxy is a worthy replacement. I can't really comment, as I have not really used either.
I don't have extensive statistics to back it up, but my impression is that they are usually ok. Well within GOG norms. Bugs occur, but they are still the exception.