I've been meaning to try something like this at work for training and documentation. Haven't yet, but here's the previous discussion of showterm:

https://news.ycombinator.com/item?id=6190600

A couple of interesting repositories mentioned in that discussion:

https://github.com/chjj/term.js

https://github.com/chjj/tty.js

There was also mention of ascii.io (currently unreachable) and shelr.tv (domain squatter).