You're right Exilent, quite similar to Rbm towerhawk but with many differences.
Like you I think many Amiga towers were Pc cases hand-made converted by small companies..
About my Gift, I bought it many years ago from Poland, shipping cost was a real blood loss for me

I had an Infinitiv and I was probably one of the first Italian who bought it (it was so "tough" that I was always scared when touching it

)
So this Gift tower was a real upgrade.
As far as I know Gift was a small Polish company producing Amiga stuff (ie a keyboard adapter Lyra-like)
The only Gift tower I ever saw was the one you reported in your last link. However mine is a Perfect Pro version, never seen another one.
It's strange that both BBOAH and Amiga resources don't mention any Gift product. Maybe some Polish guys can give us more infos about Gift..