Yes, the previous Duke died unmarried and childless.
Not a spoiler for this series, but a little bit of trivia I came across on Wikipedia when looking to see if the elder son we saw in ep 1 is the current Duke - no, he isn't, he died about 20 years ago at the age of 63. Had open heart surgery and died from complications. His son is the current Duke. Anyway, back in the mid 70s there was a fire at the castle and the elder son was Duke by then, so had to find the money for repairs. He sent out an urgent appeal to all the members of Clan Campbell worldwide for donations. Many responded. Shortly afterwards the British press reported that the Duke of Argyll was one of the wealthiest people in the country. Many Campbells worldwide wrote in asking for their money back.
The greed, entitlement and arrogance of the aristocracy knows no bounds.
Enjoyed this so far. As I see the whole thing is available on i player, we'll probably watch ep 2 tonight rather than wait for next Sunday.