Here's a quick description of four video games that I think had a big impact on my taste in games growing up, and what it is about those four games that went on to define my taste in games, in the order I first played them.
Flimbo's Quest (c64)
A platforming game where you're armed with a weapon the approximate strength of a peashooter. You start each level at a shop in the middle of the level and have a bounty - a specific glowing enemy. Track down and kill the bounty is to collect the letter of the password it carries, and take said letter back to the shop. Repeat until you have the full password for that level, then move on to the next level. The more you play each level, the more you'll start to learn where bounty versions of each enemy that might appear at the bottom of the screen can spawn, and the location of the two treasure rooms hidden in each level. The strict 20-minute time limit has aged like milk left out in the sun, however.
I think this set out my base expectations of what a video game is to me. It wasn't the first video game I played, but it is the game that solidified to me the appeal - Existing in a virtual space that, on some level, makes sense in its own right. It's also an example of exploration - but at a very mild level. It also set a baseline expectation for how video game music should sound - melodic and hummable. My tastes for that have expanded since then but I'm happiest with video game music when I can enjoy singing along to it.
Treasure Island Dizzy (c64)
Adventure game/platformer hybrid where you play as an egg. Explore the two islands and underwater region, collect items to solve puzzles, while avoiding deadly traps. This game has probably aged the worst of all titles on this list, with its single life, bizarre jump designed more around showing off a sprite rotation algorithm than gameplay, and queue-based inventory system. And despite all of that I can't help but fundamentally enjoy this specific entry in the franchise over all others, with only the jump physics not made sensible in other entries.
This solidified everything about what Flimbo's Quest taught me to expect from games, though the music isn't nearly as good, with even more emphasis on exploration and a setting makes sense. It also is the game that perhaps divorced any idea that being good at a game is necessary to enjoy it, being full of obtuse puzzles and design elements of questionable fairness.
Sonic the Hedgehog (Mega Drive)
Action Platforming with an emphasis on maintaining momentum, which rewards good play with the opportunity to go fast. Overlapping pathways throughout zones help sell them as real, lived in, places. There are some issues with the first entry in the franchise - Marble Zone is perhaps a little too linear, Labyrinth Zone is a mess, and the lack of spin dash and/or super peel out makes it feel fairly sluggish compared to later entries.
This game set, on some level, expectations that playing well would reward you with gameplay that feels good rather than something extrinsic. The combination of lots of hidden areas with goodies inside and multiple routes to figure out the best via trial and error rewards exploring the zones at your leisure, further solidified an enjoyment of exploration in virtual spaces. Looking at these three games in combination drives home where my love of exploration in games came from.
Sim City (Snes)
Build a city to your desires and whatever constraints the map you selected places on you. Be sure to maintain your residents needs to ensure you continue to have enough cash to operate with. Also contains six scenarios where you go into a pre-existing city and try and fix its problems. This version of the game had far clunkier controls than on PC, and the simulation was a lot simpler than in future instalments in the franchise, but neither of those particularly negatively impacted my enjoyment of it.
I think this is the game that convinced me that management games are fun. I had played some before but adding a spatial element really made the genre click for me. I think Sim City also served as my gateway into strategy games generally, and with that my preference for slower-paced titles over action titles. It may have influenced my taste in board games more than video games. Give me tabletop games where I can build my own little sandcastle in front of me that then does things that influence my efficiency to improve on that sandcastle and I'm happy, especially if building it lays out spatial constraints restricting my ability to expand it.