I think you are asking what system runs this forum and sets-up those activity summary emails, right?
We use discourse here. An open-source discussion forum software. The specific feature I think you're referring to is this:
I am happy to hear you like this feature!
I will say the summary is a site-level summary. For what it's worth, I always felt that -- with all the niche sub-communities here - it might be nicer to offer folks more customization over what they get updated on. That is, being able to focus on Shiny content or R-Admins content, and ignore stuff you don't care so much about.