In terms of replay value and intricacy, 'computer games' are arguably several largely different things that all just happen to be amenable to running on computers and being sold in software boxes:
The trivial analog to simple games is (of course) those games implemented on a computer. Being the trivial case, this is mostly a wiseass cop-out; but it's worth mentioning because computer implementations have made a substantial difference in what games are considered 'solved' and how strongly. Some games are so simple that children can solve them by hand (tic-tac-toe, most notably, since people do actually play it; but it's simple enough that most players eventually solve it and lose interest); but solving checkers, or the partial solutions for chess and go, are exercises that require ingenuity and cunning; but a lot
of brute force.
The slightly less trivial analog is extensions of classic games that would be impossible or impractical to fabricate as board games. Mostly 2d games adapted to 3 or more dimensions(or 3d puzzles, like Rubik's cubes adapted to 4 or more
dimensions). These usually have some improvised implementation that doesn't need a computer (multiple chess/checkers boards with rules for pieces moving between them in the extra dimension, that sort of thing); but computers make them easier and less knock-over-and-abandon-in-frustration prone.
Then there are computer games that are really, in terms of playability and intricacy, basically team sports, rather than anything analogous to deterministic games of perfect information like chess, checkers, go, etc. Something like Counter-Strike is replayable much like soccer or football are (ignoring the fact that operating systems and Glide/OpenGL/DirectX tend to break backward compatibility more often than 'grass' does, so a single, specific, implementation
may not remain playable in the long term without porting, though games with robust port support are in decent shape). There is strategy and teamwork; along with individual expertise in implementation, so most of the 'churn' in these games is either abandonment of older engines in favor of nicer ones, or iterative tweaking of weapons and balance. Specific 'games' in the sense of 'Program X sold under name Y' tend to come and go; but the overall dynamic is similar to regional variations, changes in equipment, occasional rule tweaks, and the like in traditional sports, except that traditional sports tend to treat variants as all being flavors of A Sport, while the trademark and SKU-focused game market tends to treat each variant as a separate game.
Then there are the 'games' that really shade into choose-your-own-adventure books with pictures, or movies with reflex tests: I enjoy these myself, and they are a perfectly valid form of entertainment; but they are about as dissimilar from classic 'games' as something called a 'game' can be. Single-player FPSes, relatively 'closed world' RPGs, that sort of thing. Hardly identical to a film(in all but the worst excesses of the early days of "Wow, we have a whole CD
to fill with shitty, overcompressed FMV!" era), the tests of reflexes, RPG party management, or whatever are genuinely part of the experience; but they aren't terribly replayable because, sooner or later, you run up against the fact that there is only so much manually-generated, written, and voice-acted plot to uncover. Likely good for more than one playthrough, unless brutally linear; but each 'branch' costs so much dev and artist time that there aren't going to be too many of them.
There may also be a category for the games (the Civilization series being the most prominent example that comes to mind) that could
have been implemented as board games; but would be near insanity if you had to keep track of teeny plastic wheat counters for every single square. If these are single player, they often wear out their welcome sooner or later because the AI opponents just aren't good enough (whether because there just wasn't anything in the budget for 'hire academic computer scientists to do deep analysis of the game and attempt to solve it', which there isn't, or because the game may not be solvable in any remotely computationally tractable way); but against humans these might qualify as both genuinely somewhat novel, and genuinely replayable and intricate, it will be interesting to see.
'Emergent' games (like DF), may or may not be sufficiently mature; but if they do end up standing the test of time and intricate replayability, that would be the most novel of all, since (unlike games that attempt, with varying levels of success, to make an AI do a human's job) these games tend to give the NPCs fairly limited intelligence; but enough room for the world as a whole to just go nuts in interesting ways. That has not historically been possible in games; but it is also not an imitation (however accurate or inaccurate) of a human opponent or opponents, as with 'Chess-but with someone who's always up for a game!' type computer games.