I mean, I don't think EA can barge in and demand you prove you bought a copy of Dungeon Keeper back in the day (or since), just because you're running KeeperFX.
I think the practical matter is mainly that KeeperFX can't redistribute the artwork and levels themselves. So, as another user said, you need to copy over the files from GOG or a CD, etc.
From an engineering POV it's great that it no longer needs to call into the old executable; they may be able to drop some legacy code and change some internal types, clearing the road to more changes in the future.
Generally game assets don't depend on the external environment like code does. Sure, porting is still a lot of work (which I don't think has been done for this one), but it's less work than porting an arbitrary executable.
But most importantly, not everything has to be a product with a practical benefit for the user, if the project goal is to be able to be a drop in replacement for all the code, and it does it, and the people involved are fulfilled, that is perfectly enough.
Say, maps where limited to 85x85 slabs up until now, but in KeeperFX we allow maps up to 170x170 slabs in size.
IIRC GOG runs the DOS version of Dungeon Keeper on DOSBox, because the Windows version doesn't run on modern Windows. This means users miss out on the higher quality graphics mode.
There are also improvements to the user interface that weren't a part of the original.
Same goes for many other remakes.
The big change is that the game does not use the functions from the original game to run anymore. All previous versions used a dll made from the original game as a crutch, so players would have the full experience on a partly made remake. This made the game fully playable from day 1, but it also meant we were limited in a big way in what kind of changes we could make. For example if Dungeon Keeper believed there were only 32 types of creatures, KeeperFX could not push anything related to a 33th creature type to the original DLL which meant we just had 32 creature types too. Now the number of creatures types comes from a user editable config file.
tldr: KeeperFX is there to make DK better, it does not make free.
You don’t have a purchase/download option available to only acquire the assets, so you’ll inevitably purchase & download original assets + original executable, discard the original executable and use original assets + keeperfx executable.
Or you’ll acquire the original assets alone through nefarious means and can then just use it with the keeperfx executable.
Technically I don’t think you can be requested to provide proof of ownership, but keeperfx can definitely be taken down for distribution of assets they don’t own. So the acquisition of those assets falls on you to resolve and is outside their concern. They can only recommend you to purchase the rights to those assets from the proper rights-holders.