I just thank people in person when the meeting is over. I don't see anything in that article that explains why I need to send an email, too.
I suggest you talk to someone in a position where curating relationships is key - founders, growth, agents - and see what they have to say about follow-up emails!
I'd say the advantages are: Show gratitude, reduce the hurdle for the other person to ask questions/reach out via email in the future, summarize the most important points made, stay top of mind with the person...