Examples include: Scary Game Squad, Gamegrumps, Team Double Dragon, and the like.
I just find let's plays a lot more entertaining when multiple people are playing and chatting than when it's just one person rambling. But these are weirdly hard to search for!
If you take a little time to get into them, the early "Let's Game it out" videos are hilarious. e.g. https://www.youtube.com/watch?v=1RPEtoJ9ZA8