Photoshop isn't on the web, but I oppose closed source in principle.
> Should they give away their source code?
Ideally, yes. If you do it is still your decision, but you still should be aware that if you introduce truly new concepts, someone will clean-room reverse them, and publish them.
> So, art programs kind of need source protection.
The Krita project begs to differ.
> I won't be making a web-version until this is the case. If you can crack NW.js source protection, let me know
Then you shouldn't make any build where the business code runs on the client. Even native binaries can be reversed, their functionality analyzed, and copied. Which is how LibreOffice/OpenOffice originally discovered how to parse the Microsoft Office formats.