Considering that US GDP is 8 times that of Russia, I would expect the Russians to be a little bit more annoyed than an American if the American spend is only three times theirs.
Military spending isn't proportionate to a GDP. The two have little correlation, as you can see in countries like N. Korea, former Soviet Union, Ba'athist Iraq, etc.
But let's assume your logic is sound and we'll make a comparison. China's GDP (2013) is $8 TN, but they still only assign just over 1.5% of that to military expenditures. America's GDP in 2013 was $15.6 TN, but we allocated approx. 4%; around 2.25 times the amount of China. Even if we're using "proportionate spending" logic, wouldn't China's expenditure be closer to $320 BN? Yet they spend only 2/3 that amount.
I don't think any military analyst in the world would say China is not "safe from terrorism" or is under any risk of invasion from a foreign power. They don't have any issues with Islamic terrorism and haven't been sucked into the Middle East conflict. They're obviously doing something right with domestic and foreign policy, and doing it with a lot less money, too.