The Linux minimum and recommended requirements list specific Nvidia graphics cards. Is this a hard requirement for Nvidia branded cards, or just for Vulkan 1.1?

Well, it is sad but the requirements are frequently so short that they lose meaning.
Of cause one is not in need of an Nvidia card - especially under Linux this would not be reasonable.
It should be read as "NVidia GTX 750 or similar graphics card" - so it indicates a generation/capability to play.

I am playing with AMD Navi 10 (aka AMD Radeon RX 5700 XT) Vulkan 1.2 without any problem.
But as Steam and GOG do list the same requirements it may come from the Devs - and a Vulkan version is not given.
So should work on any Vulkan implementation (but maybe it must be conformant ...).

In case you want to get a more specific answer you may ask the Devs: support@pillowcastlegames.com
If you do please put the info here so all can get the Devs statement.
I somewhat used to it and just ask in case the specification does not make sense ... and got mixed results.

But I hope this helps.

In case the data point is interesting for anyone, the game runs with Intel HD 5500 integrated laptop graphics, but at a rather low frame rate even at lowest quatliy settings / 720p. On Windows, that is.