One of the things I'm liking about EVE is that the game is very undemanding in terms of your interaction with the controls. You don't click stuff as often as in most games.
Your first fights consist of targeting the enemy, turning your laser on and hitting Orbit. Then you watch the spaceships shoot each other until either you win or you decide to run away.
I haven't had that in WOW since my paladin was about 40 and I used to kill mobs by starting autoattack then reading my book until the combat noises stopped. It's a playstyle I like.
The next big thing is that a considerable amount of gameplay is passive. Real world time, not played time counts for a lot.
Your character is mainly defined by his/her skills. Skills accrue at a certain rate reardless of whether you play or not.
At the time of writing I am learning Astrogeology to level 4. Each level improves my mining by 5%. It will finish in 15 hours, 46 minutes regardless of anything I do. I'm actually going to watch football tonight and while I am not playing I know that my character will be diligently studying his textbooks. Tomorrow I will be a better miner.
I have made a trading alt. She just sits at the biggest trading hub with a large amount of Buy Orders aimed at picking up skill books that players sell off at cheap prices and a number of Sell Orders for books that I've managed to obtain at prices which are pretty expensive. It's very much a passive process. Logging in and jumping up and down won't make people buy any quicker. So I just log her on once a day, update her orders, count my money and go back to playing my main again.
The game's travel system is also fairly relaxing. To travel from solar system to solar system you Set Destination for where you want to go then your route will show on your Overview as a yellow highlight. So I just look at the stargates listed, click the yellow one then click Warp To. 30 seconds later I'm there and I click Jump. Rinse and repeat until you arrive.
Alternatively there's an even lazier way to do it. Set Destination and click Autopilot. Twenty minutes later you come back and find the ship in the Destination system.
In High Security space travel is pretty safe. I've been ganked once in High Security space. I had a load of valuable implants and skillbooks on my trader alt and had actually fallen asleep with her on autopilot. I woke up a couple of hours later and she had been suicide ganked. Someone had checked her cargo with a cargo scanner, spotted that it was pretty valuable, murdered her, got killed by the police, then had a friend steal the cargo from the debris of our ships. Serves me right really, since then I keep her items inside a container when I fly her around trading.
In low sec I've been ganked a few times now, mostly because I've had a long trip and have afked or alt tabbed with autopilot on. Some of the journeys I make are long trips with one low sec system on the way. It's crossing that place that is the problem.
Generally autopilot in high sec is pretty safe. And even the paying attention way of playing is about 2 clicks per minute. So very much a non-twitch playstyle so far.
All in all Eve feels like it automates much of the busy work that you find in games designed, dare I say it, primarily for younger audiences.