Easy modding helps a ton, but what really keeps a game alive is releasing the source code so that it can be updated by the community (or, in rare cases like Daggerfall Unity, some absolute mad lad spending over a decade reverse engineering the game and remaking the entire thing from scratch). The list is endless - the multitude of Doom versions, OpenMW for Morrowind, OpenJK for Jedi Outcast and Academy, even OpenJKDF2 for Jedi Knight 1, OpenRCT2 for Rollercoaster Tycoon, 1.13 and Stracciatella for Jagged Alliance 2, and so on and so forth. Without these modern source ports/remakes, the games would be nowhere near as popular as they are.

Also worth noting that new games not checking these boxes is not a failure, it's by design. Publishers don't want you happily playing old games, because then you'd have less of a reason to buy new ones.