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Twilight would probably play games with a story since she likes to read, and RPGs tend to be known for that. That could also include some adventure games with a large story behind it (e.g., Legend of Zelda). Of course, she's a planner which seems to make strategy and puzzle games appealing (however, I'd doubt that they'd be real-time. Probably turn-based.) Planning and acting on plans under pressure? Seems more of something that would cause her anxiety.
Also with her love of planning and making everything run in a certain way, I think she'd lose a lot of time with simulation games of a sort. RollerCoaster Tycoon? Running an amusement park? Again, she might lose a lot of time to it, but I don't know how much she'd enjoy it if things began to go poorly.
Applejack doesn't seem like she'd want to spend a lot of time on video games, so she'd probably end up playing and enjoying games that didn't involve a lot of time or commitment. She's competitive and considers herself an athlete, but I'm not sure if she's the one to make the transition to racing video games. I think she'd just say that she's rather play the sport herself.
Something as foreign as racing a car might be appealing though. It's not something that takes up a lot of time or commitment if you don't want it to, it gives you plenty of ways to be competitive with friends, drones, or playing online, and racing at those speeds in Equestria isn't a concept ponies would know about or could easily recreate (especially Earth Ponies.)
Now Rainbow Dash could probably get behind sports games more. Applejack is an athlete more by trade than by hobby. Dash loves competition, even in games, so she'd probably enjoy sports games more than Applejack. She'd like racing games as well. So even though she loves flying, if she's feeling lazy, she could still race without exerting herself.
Dash also seems to get a kick out of creepy stuff (or at least scaring people and performing in the face of danger when she isn't bluffing. ) She might enjoy some stealth games or horror games. I think stealth might be a little taxing, because Rainbow Dash hates waiting for long. She'd just want to act and would likely fail pretty often (Which she also hates.)
Fluttershy would play Kirby and Pokémon. I feel like she would love seeing a cute, adorable creature annihilate all of the competition. And Kirby has recently been more of a relaxing game than one that requires a lot of effort and practice. Between what I've seen and heard of Return to Dreamland and playing Epic Yarn, they are almost interactive art as much as a game. Sounds like fun. Of course, I think she'd like catching different animals, and Pokémon has always been a solid monster-catching RPG.
I also feel like she'd be more likely to play specific games than games from a particular genre. She likes pretty much all animals even though they're all very different, so I feel like she'd like a certain aspect of a game and would enjoy it for that. It might be found in a shooter if the enemies were inanimate and exploded into something harmless and floaty. It could be found in a RPG if she really likes the characters and wants to take care of them. They'd also probably be single-player games. I don't think she'd want to play with people she didn't know, and she'd probably would be too concerned about beating her friends and making them feel bad to play with anyone else.
Rarity. Enjoys creating fashion and being fashionable. Very sophisticated. Generous to a fault.
That doesn't sound like a gamer at all!
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Anyway, I can't think of many games that she would want to play. Perhaps a simulation game where she can run a business or, again, a game with a story behind it. She likes scuttlebutt and gossip, so she might enjoy games where the story is compelling and there is a good bit of romance (cheesy or well-developed and realistic.)
There's also a chance that she might take pride in beating up a character. I've always said that Rarity is a classy pony by nature, but she has the ability to be really athletic (outside of comedic situations and gags. Carrying Tom was more of a gag as pretty much anyone could carry him.) Think about it. She kicked a manticore without a second thought, she very swiftly hip-checked Twilight with little effort, and performed really well at the Sisterhooves Social.
If I think back to one of my favorite comics*, then I think she might like first-person shooters with a touch of stealth. Sizing up a situation, getting into position, and executing objectives flawlessly. I think she might enjoy something like that, and I think I can allow myself a little bit of headcanon here and there.
*And if you don't know about the Time Off comics, especially the Rarity one, then shame. On. You.
Pinkie needs something happy, upbeat, and nothing that takes a lot of time to get into or thought. Not that I think Pinkie isn't smart. On the contrary, I think she can make relatively sound decisions more quickly than any other pony (her values that go into those decisions may be suspect, but they often work for her.) But I don't think creating a whole strategy and ongoing tactics for one map would be something that she'd enjoy.
Something interactive like dancing games would seem to be up to her speed, as well as a lot of multiplayer games. Mario Party seems like it would be made for Pinkie Pie.
I think she'd also enjoy games that are as much art as they are a challenge. She seems to enjoy things that stimulate her senses (e.g., eating a ton, smelling flowers, watching butterflies, rolling around in the grass, singing for the smallest of reasons). Video games only hit on three of those, but if you had a game like Electroplankton, (I had another in mind, but I can't think of the name,) Pinkie might be entertained by that without actually having to accomplish anything.
EDIT Seeing as long as my post is, Explosive ninja'd me without seeing what I posted. Not only did we come up with specific games that were the same many characters (I actually considered using AJ's accent in a hypothetical quote from her,) we listed the characters in the same order.
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Don't do that again. I'm paranoid and sh!t.