I believe I ran into the same thing. If the other commenter is anything like me, the underlying cause is that `delta` did not support unified diffs until version 0.0.15 (ie only for the last 6 months).
I don't even remember when I installed delta the first time, since I ultimately liked ydiff better for side-by-side diffing with line-numbers. I thought I'd give delta a try again only because of this fzf endorsement of it (context is a little different, too, obviously).
My perfect diff tooling would support both drop-in replacement for `diff` but unfortunately I still haven't found the one that checks all the feature boxes I want yet. But this fzf wrapper is AWESOME! I tried to do something similar a few months ago and ran out of steam. Glad you didn't!
Anyway, updating delta to latest did the trick for me. Note that if you are using homebrew, the formula name is git-delta
https://github.com/bigH/dotfiles/blob/master/configs/core.sh...
In the meanwhile, I'll try to repro.