Like any other company's engineering blog, a post like this can help with recruiting and it's also a nice way for the team to summarize and share what they built.
It's also relevant to the NYT's goal of surviving the digital shift. Giving the world a peek under the hood isn't just an interesting story, it's brand-building for a publication that wants to be seen as modern.
Open sourcing it is a good suggestion and one that some have made previously. Open sourcing it requires a fair amount of work to remove company-specific, internal stuff and making it easy for others to install, upgrade and maintain it on their own. That fair amount of work hasn't yet made it high on a priority list, but let us hope it will :-)
It should be known that I love behind-the-scenes more than the movies, and I love these peeks more than anything else. Just was genuinely curious why NYTimes would take the time to show us. I don't think it would help any with the subscriptions/circulation numbers but I am probably wrong.