I can speak only from designing mobile web apps, but I imagine the same holds true for mobile games. What I’ve noticed is that mobile users have short attention spans, largely due to things like being easily distracted by the environment (limitation of things outside their control). Of course, this makes sense. When I’m riding the subway, my signal cuts in and out, so I can’t really use an app that requires constant connection. If I’m out in public, there are noises and other distractions. In general, if I’m using my phone I have some time constraint (the subway ride will end, I have to move over when new people get on, etc.).
I cannot devote my full attention to the app on mobile, even if I want to. This is the fundamental difference between designing for mobile and designing for computers.
I think tablets fit somewhere in between. You aren't usually as distracted as you are on your phone, but I think it is one of the reasons you don't see very AAA style games that require a ton of attention (could you imagine playing EQ on a tablet? FFXI?) I'm sure this will change in the next few years, but for now the way people use tablets and the way people use PCs are much different. There are many successful games out now that do require a lot of constant attention, but by their nature tablets are much less constrained than PCs - I might want to go lay in bed, or sit in a chair, or pace around in circles in the middle of playing a game on tablet. Tablets (and mobile) enable a much greater range of physical freedom than PC games do, so it's not surprising that games are played differently.
I think games like HayDay are incredibly popular because they recognize this and exploit it.
HayDay is optimized to do two things:
This works incredibly well, because I can get a meaningful experience after playing for 30 seconds when I’m waiting in line and I don’t need to have my full attention on it. It’s designed to keep you coming back at different intervals. Extended play sessions are certainly possible, but they are not a goal of the fundamental design.
This is not negative. You typically play mobile games in a distracting environment, and it's hard to think when you're distracted. I shouldn't be required to think in a casual game, because I'm playing it casually. I should not be required to hold anything in my memory to do a specific task. I shouldn't have to jump through hoops to bake bread.
This isn't to say you can't have complex gameplay. My point is that actions you take to achieve it should be stupid simple for mobile. I should be able to fantasize about building the perfect gnome pathing, or the best layout, but the actions I take to do it should be simple.