It's definitely not categorically malpractice to not use Word. Depends entirely on the situation. If a court demands docx and you file an rtf, or you refuse to read a client's redlines because they're in Word, sure, that could be malpractice.
The only proprietary software that I think _might_ be malpractice not to use is a legal research service with a capable citator, like Westlaw or LexisNexis. If you rely on a case that was overruled, you can't defend a malpractice suit by saying, "I didn't want to pay for the software."
I hear CourtListener (a free legal research tool) is working on a citator--hopefully it's competitive with the paid services.
Some courts expect Word format. I haven't been close to litigation in ages so I don't know how common a thing this is, but here's an example of an apparent "Word only" federal court: https://www.caed.uscourts.gov/caednew/index.cfm/attorney-inf... . So sure, in a hypothetical where a lawyer stubbornly refused to use Word in the context of a filing in that court, you can imagine consequences arising to the level of malpractice, but I don't think that's what they had in mind.
A more familiar issue to me (and I'm guessing what that speaker was thinking of) is that if you're negotiating an agreement with some other party, and they are using Word (as they most likely will be), it is going to be highly inconvenient at best to insist on using some alternative tool.
Red Hat's in house legal team is, er, was not a law firm of course, but ages ago Red Hat attempted to have as many 'back-office' staff use RHEL as possible, with few exceptions related to what was necessary for regulatory purposes. This extended to Red Hat's legal team, which attempted valiantly for a while to use OpenOffice (as was, and I suppose more specifically the RHEL packaging of the go-oo fork in those days) for all document-related purposes, including negotiating agreements with outside parties who were using Word. This proved to be impractical for at least the subset of the legal team that did that sort of work as their daily bread and butter, and eventually they got access to Word on Windows on VMware. Later on, it became possible for Red Hat lawyers to use OS X and Windows with Word, so the issue went away.
As a techy person with a law degree that doesn't really practice any more, the "silos" of what each lawyer thinks is and isn't a "must have" is interesting, as well as the huge differences in rates and types of tech adoption; a huge factor here is probably administrative assistants who do a lot of heavy lifting.
Wordcraft is now a decent Word clone and is leaps and bounds over OpenOffice.