I voted no but with the following addendum... you don't have to be "interested in" a SOs employment in terms of understanding specifically what he does... the ins and outs of the business, etc. However, you should, as any "spouse/BF/GF" should... be interested in his job in terms of how his day went... allowing him/her to brag about the business, what he does, etc. and lending an ear when he wants to talk about things good or bad.
That's what we're here for.
I think it's the same for any topic.
I can remember a specific instance that SO pissed me off with my spouse. My two younger brothers play in a serious, organized rough-touch football league. They're very athletic, very good, and a pleasure to watch play.
One night, I had gone to see one of their games. The next day, I was talking about the previous night with her, talking about how well they did and how much fun it was to still watch them play.
I was off-handedly dismissed with an "I really don't care."
Gee, thanks for a few minutes of your time to just quietly nod and be receptive to my excitement about it.
I would never expect her to be interested in the game. However, I would expect her to listen to my experience and how exciting/fun it was to still watch them play. There is a difference. It's the same reason why I listen to things like the events and "Party Lite" candle demonstrations... the particulars of disagreements with her sister, etc. You lend an ear. You show an interest in how they are feeling at a particular moment, even if you don't actually "care" about Party Lite candles or what, specifically, the sister did to piss her off today.
That's my long-version answer to the query.