Why would anyone downvote you for asking such a complex question?
What makes a game tick for me is whether it feels like a pronounced, unique installment that is greater than the sum of its parts, and whether or not it's just piggybacking on the success of everything that already exists (read: these copious amounts of World War 2 games and brown-colored first-person shooters) or whether it's forged its own path and the developers did something they truly love and enjoy, themselves. If you love what you're making, it WILL show through. Every single time.
When game development solely becomes a business decision or a "me too" bandwagon, you might as well get out of the industry, because you'll probably have no interesting ideas or experiences to offer (and oddly, will probably make less money in the long haul). Movie to video game re-imaginings come to mind here.
The best way to answer what makes a video game good is to tell you what video games I thought were good, and maybe even research them yourself.
Grim Fandango is my favorite game of all time. Sure, it's an adventure game with a somewhat unwieldy keyboard control scheme and an awkward "hot-skull" interaction system, but the pre-rendered visuals dripping with artistic decor and the borderline insane premise of the game, coupled with incredibly fitting voice acting just brought everything alive for me. Even if I play it to this day I'm impressed with it, despite the fact that I know how to beat every single puzzle in order.
The Splinter Cell franchise helped challenge mindless, tedious shooting games with "What if I could take out an entire building of guards without firing a single shot by keeping to the shadows?" Granted, not the first stealth game, but before they wrecked the franchise with Double Agent and Conviction, they proved they knew what it took to make stealth fun. And if you think about it, you could almost consider it a puzzle game in a roundabout sort of way, despite having a deep basis in violence and subterfuge.
But a good game can be about more than just doing what hasn't been done. You can do what has been done, and in addition to doing it better and setting a new standard, add a twist or two all your own. Were it not for Bulletstorm's skillshot system and hilariously unexpected, overly-juvenile humor, it'd be just another "rawr, muscular mercenary goes around and shoots dudes" game. But they melded the elements together well and created a unique experience.
Replayability is huge (for many people, at any rate). I've never in my life spent full price on something I thought I would only play one time.
Resident Evil 4's method of enticing you to play repeatedly had me completely caught off guard. Let's face it, the game was super linear. Were it not for the simple fact that they allowed you to keep all your weapons, money, and upgrades on to the next playthrough, I wouldn't have even bothered replaying it. But because I knew I would gradually get more and more bad-ass, I greatly enjoyed playing through it 4 times while I upgraded and crammed everything I could into my inventory, which I happily used to blow the smirks off everyone's face on subsequent playthroughs where it's actually fun to blow through it being overpowered, since you've already ingested the storyline.
You have to be able to get addicted sometimes, especially when you talk about old-style games. Think about what made you persist through even a few games that had you frustrated at many times. It could be as simple as something that feels cathartic, like an awesome kinetic sound effects, hearing a character's voice, or knowing an upgrade or improvement is right around the corner.
