Mainframe computers allowed multiple users to connect and "time-share" the mainframe using terminals. Terminals could connect using telephone landlines and several universities set up networks of terminals in libraries and schools. The first public network was the Dartmouth Time Sharing System (1963-1999) and the earliest games were written in FORTRAN and Dartmouth BASIC. Games originally had to be customised for each type of terminal but in 1978 the "curses" library introduced the ability to write universal code. Companies like Compuserve also sold mainframe access but eventually terminals were replaced by personal computers.
Mine Field (1975)
Minefield (198x)
COBOL Minesweeper (2010)
Cobol-Minesweeper (2013)
CoinBoller (2014)