Don't see it anywhere and store page says Deluxe Edition has it.

Should be in your library. Look at the attached screenshot.

I thought it should be there but it's not for me -> screenshot

That's strange. Check if you're allowed to download the artbook from this link:

https://www.gog.com/downloads/dlc_desperados_iii_artbook/86788

You should contact GOG support as well. I guess something went wrong on their side.

You can also try to refresh your account:

https://www.gog.com/account/refresh

Thanks. Refreshing actually worked :)

And yeah I contacted GOG support some time ago but they are overloaded with tickets so waiting for a response may take like forever from what I got from an automated reply.

EDIT:

Well, I can see it in bonus section now but I'm getting error 404 when trying to download...

Try if this link is working for you:

https://www.gog.com/downlink/dlc_desperados_iii_artbook/86788

If not you'll have to wait for a reply from GOG support.

Seems fixed. All links work now. Thx.

You're welcome. :)