Yes it supports direct x 9 and any screen resolution except maybe higher than 1920x1080.
You will be able to play most games with this setup.
There are some gameplay videos on youtube of highly graphical games being played on intel 4600 hd graphics such as farcry 4 and Battlefield 4 on an i5/i7 processor and all of them run smoothly (around 30 fps).Yes they are on lower graphics settings but the game still looks good.
Game developers understand that there are many laptops and some desktops using intels integrated graphics, so they cant ignore them. They have to cater to the casual gaming audience too, not just the hardcore gamers with thier multi monitor setups getting insane field of view.
As long as you get a laptop with an i3,i5 or i7 and at least 4 gb ram, you will be okay.
Just make sure you get at least the hd 4000 graphics or newer. Anything older will not be able to run modern games, if that is what you are planning on doing.
I recommend the intel 4600 hd graphics if you are planning on playing games.