First of all: check your temperature of Graphic card and CPU (im bios or using program)
Then check in BIOS, because maybe there is something like a RESET temperature.. you know what i mean?
Its to protect computer from burn... In example: At temperature of CPU - at 92* your computer is restarting...
But remember, dont change BIOS settings which you dont understand.. you can f*** your computer up...
As i said im not n00b in hardware part of informatic... :P
Im studying informatic at my High School, and in 2 years im going to study it at our Collage

Anyways.. back on topic

Check that please, and write here your temperature.
Well, most likely its up to graphic card...Nah full screen has nothing to do with it..But also yeah, i could start some games without restarting and after 15 mins again restart :P
EDIT: It dont have to be graphic card... when its graphic card or RAM memory, there should be blue screen with white letters, before computer restart... It can be ATX also, but im pretty sure thats something with CPU..
And Brains - in your case, im sure thats case of temperature

Some games are making CPU hard-working, so he is getting warm, and temperature up... i think new CPU Fan with more RPM should solve your problem.
Why it restart only on "some" games? Not all games make your CPU or Graphic card, hard-working..