Some I don't see mentioned yet:
- Simon Tatham's Portable Puzzle Collection ported to pretty much everything.
- Nethack (and its variants), Dungeon Crawl Stone Soup and Brogue are great roguelikes.
- For boardgame fans the original Keldon AI for Race for the Galaxy is open source and works very well on Linux.
- Fish Fillets NG is one I have fond memories of from many years ago.
- The Ur-Quan Masters is Star Control 2, another classic.
This sounds similar to SLIME (and its fork SLY) for Common Lisp. These tools use their own protocols rather than LSP in part because they pre-date LSP but also because LSP is not a good match for everything they do. In addition to the usual LSP functionality like symbol lookup, xref and completion they also provide a very good Lisp REPL. It is easy to have the server side (called swank) running as part of an existing service which sounds a lot like what the post describes. For example I've used SLIME to connect to my live StumpWM sessions.