You might not be playing on maxed out settings with extremely GPU intensive games, but you can easily run the most demanding of modern games on medium to high settings with that. It should run Skyrim at or near to Ultra, and FC3 on high settings.
I've got a $250 Asus with an Intel Pentium 2.3ghz B970 APU, 4gb DDR3, and 320gb HDD and it runs Skyrim, Burnout Paradise, Serious Sam HD, Shadow Warrior, Saint's Row 2, Fallout 3 with lots of mods, and Farcry 3 on low-medium settings depending on the game at around 30-35fps if not more.
I don't use it for gaming much and mostly use it for browsing the web while I'm using my big PC for other things like games, streaming video, or when I'm watching television because my monitor is also my TV. It's a pretty low end laptop and it will run most modern games even if only at low settings. There are some games I can't run on it, but those are only a few extremely demanding titles.
Sometimes I game on it if I visit family and I'm away from my PC or end up in a waiting room for a while at a doctor's office or something. It's primarily for browsing and video streaming though. It's very convenient to have and only weighs about 3 lbs.
That Alienware laptop you're talking about is far, far more powerful than what I've got and should run those games with no difficulty whatsoever at decent if not maxed out settings no problem.
You're good to go with that laptop. It could run Crysis 3, the newest Call of Duty, Max Payne 3, or Battlefield 4 without issue at decent settings and those are much more demanding games than Skyrim or Far Cry 3.