That's right, US also has many hiding budget. For example, her space program simply doesn't count as the fund for the military expenditure.
However, the official figure of the military budget is just some playing number for the political purpose, who has more money, so who will spend more, it is logical.
Just because China consider's its space program for violent (i.e. military) purposes doesn't mean other countries do. NASA is for the exploration of space, the advancement of humanity, and innovation that effects all parts of our lives.
Don't believe its about exploration? Our probes have reached to the edge of the solar system and beyond, there is your proof.
Our rovers are still present on mars, with more to come.
Our entrepreneurs make leaps and bounds when it comes to bringing down the cost of manned space travel, to their own profit, but more to their own posterity.
Our businessmen will handle the now routine task of taking men to orbit, our government will focus on taking men beyond.
Even Chinese tourists will have a chance to go to orbit should they be willing to pay for a ride.
There is of course an element which considers the military dimension for space, and that is the USAF. NASA is purely civilian led and works toward the mentioned goals of exploration and innovation. There has been technological spinoffs that have benefitted the military, but it does not work for the military, and does not consider the military implications of space.