atom-text-editor { text-rendering:optimizeLegibility } makes no difference.

Working:
!= <= >= /= == ^= >>= <<= ===
... (...)

Not Working:
-> => (all lengths)
->>
!== maps to != =
>>> (and reverse)
-<< (and reverse)
***
(all arrows)

It would be safe to assume that most of the rest are not working, but those are the ones I had a chance to try.

It may be that I am typing the wrong keys? But since some of the ligatures are working, I must be doing something correct?

(One other suggestion: Why not have a plaintext version of all symbol combinations in the README.md which produce ligatures. Then someone can just copy and paste the whole set into Atom, see which ones convert or not.)