Does Kasmina, Enigma Sage replace planeswalker abilities?
I would think that all other planeswalkers gain those abilities and do not lose their own abilities.
Consider the case of Nicol Bolas, Dragon-God

Nicol Bolas, Dragon-God has all loyalty abilities of all other planeswalkers on the battlefield.

Nicol Bolas, Dragon God has a static ability similar to Kasmina, Enigma Sage's ability except it gives itself other planeswalker's abilities.  If it removed its own abilities, then the very act of printing abilities on it would be pointless.
Furthermore, Kasmina does not have the text &quot;and loses all other abilities&quot; that is present on other cards like, say for example Imprisoned in the Moon.