Chess is a leisure activity, not work, you cannot compare the impact of automation of the two.
Also, chess engines did kill chess. Chess used to be a spectacle on the national stage, from 2000 up until Queen's Gambit and the following streamer boom, chess was largely dead.
I'm extremely skeptical of the claim that engines killed mainstream interest in chess. The trend seems to only go back to 2004, which is not long enough.
My sense growing up in the 90s was that chess was a niche thing for nerds. I think it seems somewhat more mainstream now than it was then, while remaining fundamentally a niche thing for nerds :) But it seems very clear to me that it never underwent the broad collapse that I remember being broadly predicted after Kasparov vs Deep Blue.
My anecdotal recollection is that Deep Blue is a big part of what put chess into everyone's mind and rejuvenated the mainstream interest in playing what had previously been a nerd niche.
Even today, there's a handful of people who make a full living off chess. The owners of chess.com, a few streamers, a handful of super GMs, and chess teachers, and the latter will be automated away.
And prior to the explosion in popularity? Barely anyone.
My sense growing up in the 90s was that chess was a niche thing for nerds. I think it seems somewhat more mainstream now than it was then, while remaining fundamentally a niche thing for nerds :) But it seems very clear to me that it never underwent the broad collapse that I remember being broadly predicted after Kasparov vs Deep Blue.