Not the best video quality, but the following video shows that Dota 2 is running between 35 - 40 FPS on the Intel HD 4400 with graphics on high settings. Since he is likely using software to record while playing, the actual FPS when not playing should be around 15% - 20% higher.
https
/www.youtube.com/watch?v=4RKB6O1TdMc
Here's a video for CS:GO with graphics set to max. Without using FRAPS to record he gets 40 - 45 FPS.
https
/www.youtube.com/watch?v=9V4oCg9IAiE
The following 15.6" Dell Inspiron laptop for $310 from Bestbuy should be fine for those games. Note that it has a Core i3-4030u @1.9GHz CPU. The laptops in the linked videos have a core i7-4500u / Core i5-4200u so you will get a little less FPS compared to those...