This is an absolutely hilarious question--just silly enough to be amusing, and just serious enough to provoke actual consideration!
I would argue that the time of total war between nations is over, or is at least in remission, which would make this sort of economic warfare unnecessary and even undesirable. And games, while an important part of culture, are not as effective a target as agriculture, industry, or transportation assets anyway. Piracy against enemy shipping was and is quite damaging, and might warrant state sponsorship. But I don't see games being a big enough part of an economy for that to be effective. At least not yet!
Also, there is the fact that companies, at least the big multinational ones, cannot be said to 'belong' to any individual nation. We even saw this during WWII--certain factories in Germany were off-limits to Allied bombers because they were owned by American companies, even though they were building tanks and vehicles and other products for the Axis powers. German citizens often used these factories as bomb shelters because they knew the Allies wouldn't hit them. But now it's even more exaggerated.
As an example, British Petroleum is, supposedly, a 'British' corporation. But their US division, BP America, is the largest supplier of petroleum in the US and controls billions of dollars of assets. Their US division is bigger than many companies in their entirety, and despite the fact that their headquarters is located in London the majority of their profits come from the US (most of the time--currently the oil spill has made BP America a bit of a cash bleed, though the $10 billion tax write off for oil spill cleanup efforts will certainly help). So hypothetically if the US went to war with the UK, whose side would BP be on? BP would be on both sides, supplying and profiting from both. And would either side benefit from attacking BP-owned facilities? The answer is no, because if, for example, the US bombed a BP refinery in the UK, BP would simply call up its US division and jack up the prices there to make up for the loss and punish the US for attacking them.
For really big companies, it makes more sense to think of them as nations themselves, rather than members of any individual nation. Which is absolutely terrifying if you ask me, considering that the leadership structure in a big company is almost indistinguishable from that of a fascist state.
And if that $10 billion write off from BP angers you as much as it does me, here is a link to a petition where you can do something about it! http://act.credoaction.com/campaign/bp_tax_break/?rc=fb_share2
