I would immediately reject the IdeaPad U410 Ultrabook if you are looking to play games. Benchmarks have show that Intel's HD 4000 is actually a bit more powerful than the nVidia GT 610m.
The IdeaPad Y400 is a laptop and it is pretty good for games. It has a quad core CPU in case you play a game that can use more than 2 cores. The vast majority of games do not use more than 2 cores though. More importantly, it has the nVidia GT 650m which is a pretty good graphics card for the amount of money you are paying. It will do very well with a 1366x768 resolution screen; you should be able to play many games with high quality graphics and still get good performance. However, it is a heavy laptop; laptops weighing in at 5.5lbs are usually 15.6" laptops. The battery is also very low at only 3 hours.
The Asus S56CM is not a bad Ultrabook. It costs more than the Y400 because it is light. The Y400 is clearly a better gaming laptop than the Asus from the specs alone. The weight is not stated, but Ultrabooks are designed to be lighter than the average laptop. I suspect it weights in at 4.0lbs, if not a little less. However, that "lightness" means you are getting a laptop with a less powerful CPU (to conserve power) and a less powerful graphics card; the nVidia GT 635; to save power compared to a more powerful graphics card, but also to save weight because a more powerful graphics card generates more heat. That means a larger, heavier heatsink is required.
The nVidia GT 635m is actually not that weak in comparison to nVidia's previous generation graphics card. The GT 635m is marginally faster than the GT 555m which was released back in 2011. The GT 555m was considered a very good performing mainstream graphics card. My Lenovo IdeaPad Y470 has the nVidia GT 550m. It was a good graphics card back in 2011 and I still think it's performance is still pretty good today. The GT 550m can play many games at medium quality graphics with good performance and some games using high quality graphics with decent performance. The GT 635m would provide better performance than my GT 550m of course.
You need to decide what is more important to you:
1. Portability = Asus
2. Gaming Potential = Lenovo