I have tried installing fspy in blender 2.81, however it says it is 'installed' (as can be seen in attached image) but then doesn't appear in add-ons list, and hence cannot be enabled.
You installed the wrong file; you need to install
(or newer) from the Releases page.
The file you're using,
fspy-Blender-master.zip is likely the source code and doesn't work as addon.
It's not very clearly stated on the page and it's easy to download the wrong file(I had the same issue :)
The latest fSpy addon release works for blender 2.81 on Linux ( but this should also work on all other systems ).
Fspy version 1.0.3, confirmed to be working with Blender 2.81 for Windows, can be downloaded from Github