There are a number of games that are ‘born digital’. A lot of the early arcade games are good examples of this: PacMan, Space Invaders, Missile Command, etc. Those kinds of games didn’t really arise from existing, non-digital games because there’s no reasonable way even to approximate them with out a computer.

Other games were… born analog? born physical?… but seem to have found their true home in the digital world. These sorts of games are the ones with lots of counters, lots or randomizer action, and/or large territory. War games are a great example of this. You can do it with cardboard and dice, but it’s so much easier as a digital game. On top of that, the computer provides many enhancements that would have been a part of the original game were it possible – e..g fog of war, lots of highly detailed logistics tracking, true hidden units, etc. These kinds of games don’t seem limited in their digital implementation so much as limited in their physical one.

One more group to consider are those which were seeded as a physical board, card or other game, but have lead to new digital games far removed from their progenitors. One example of this is the civilization series of games (and their spin-offs). The adaption from original board game to computer game was a leap, and successive generations have moved even further from the physical game. I think World of Warcraft is another example of this kind of thing. The original step was from D&D to MUD (and probably Hack and Rogue as well). Since then the CRPG has gone through many, many iterations. They’ve also been complicated by infusions over time from the non-digital RPG world. However, though WoW grew out of that, it’s not really something that at this point could be played outside of a computer. There’s too much to keep track of and too many real time aspects. You could maybe play something that had the same feel and flavor, but the underlying game would have to be very different.