I know a video game is one I'll remember fondly when...
1. It introduces me to an interesting world
The world could be fantasy based or science fiction based, but it is a fully-realized world that persuades you to settle down and accept it as a separate reality
2. It's challenging, but not does not overwhelm me with quests or obstacles
Your mileage may vary on this, but my life is challenging enough. I can handle a little challenge, but not enough to make me question my sanity in starting or continuing the game.
3. It has Intuitive game play elements or system
If they use a new game play system (whether it's RPG based or different modes of interacting with the new world) they give you enough help to get used to it or provide you with a tutorial area to familiarize yourself. Dumping me in the world with a one page option screen can be a bit off-putting
4. It reminds me of my humanity and our connection to others
Games that make you connect to other characters to progress and then make your decisions count are winners.
5. It calls me out of myself and makes me question my assumptions
When the game presents me or my avatar with situations or decisions that I would be unlikely to face and I have to think hard about what I'm deciding
6. I learn something about myself in the decisions I make
When I leave the game thinking - I didn't know I felt like that...it's a game I'll remember.
7. When I can't stop thinking about the alternate paths I didn't take
I remember thinking about Disco Elysium, Spiritfarer, Gris or Dragon Age: Inquisition, for weeks. I'm still thinking about Dragon Age.