If you've put a lot of time into a particular Mario game, then chance are there are levels where you can enter into a state of flow, where all you have to do is run forward and you're able to time your jumps to weave your way through strings of coins, avoid hazards, and bounce of the head of enemies. Achieving this is one of the most enjoyable experience that I've had playing games, and if you've experienced it I'm sure you'll agree. It's the same goal that speedrunner look for, uninterrupted forward momentum.
Super Mario Run's design is closer to the former, but manages to achieve the feeling of the latter.
If you're not familiar, in Super Mario Run Mario is always running and you can only control when Mario jumps. There is nuance to the control, pressing your screen for longer will allow him to jump higher, and tapping again while in midair makes him do a spin that halts his descent and extends the jump. You can also jump off of walls.
This, combined with some other mechanics, allows Mario to elegantly chain bounce off of enemies, through strings of coins, and achieve that desired that of flow relatively easily. Super Mario Run gives you the thing that you've wanted from Mario games without asking for the hours of dedication that others have asked for before. Add to this the 3 difficulty levels of coin hunts as optional objectives for each level and you've got a game with depth enough that's kept me playing it pretty near constantly since it came out for Android three days ago.
While many people have really liked Super Mario Run, some are frustrated that it's not a traditional Mario experience (they do acknowledge that they understand why it can't be a traditional Mario game), but I've particularly enjoyed it because it's NOT a traditional 2D Mario game. Frankly, if I want to play a traditional Mario game, there's tons of them to choose from, even some I haven't played. Super Mario Run has offered me something new, which if they were to offer to me again for some of the stages in the next 2D Mario game, I'd be excited.
P.S. There are other feature in the game, such as the Toad Rally and the Kingdom Builder. These aren't very exciting or interesting and feel like designs from a period when they may have been flirting with a more micro-transaction oriented revenue model. However, their existence doesn't detract from the main gameplay experience, except when the tutorial takes your time to explain them to you.