There's a bunch of stuff about the huge increase in online ad revenue. I think it's a reasonable to assume that this was driven by their "digital first" approach.
Personally, having been a past subscriber to the Atlantic but given up on it owing to never having time to read magazines and only being interested in a subset of the articles in a typical issue, I like being able to read interesting stories when the mood takes me rather than piling the magazines up in the unread pile and then feeling stupid when I realize I missed a really compelling article. (I often found out about articles in my unread magazines on NPR or online.)
I have a subscription to the Atlantic because of reading the articles and their blogs online. I don't think it would be incorrect to attribute their turnaround in going digital first. I've been reading their properties for years and there was definitely a change (perhaps in just attitude).
From my point of view the quality of the journalism online made me fork over money, but I don't see how "digital first" comes into this.