The PRC has not achieved global domination yet, and alot can happen in 14-25 years.
They have been launching manned missions at a leisurely pace. Last manned launch was 2013 and before that its was intermittent as well.
I am pleased with there use of small Skylab style modules. It indicates a serious interest in Long duration space travel. However the biggest problems for the PRC taking long duration seriously is the numbers. 3 men crews are fine for flags and footprint exercises, but for real science beyond LEO you need at least a half dozen.
The next biggest problem for humans is gravity or lack thereof. That's not just pointed at the CNSA that's a across the board; thus far only the minimum of work has been done on plants and insects and mice.
larger animal studies need to be conducted to get data on the effects of artificial gravity on larger vertebrate animal. And then if successful development of a craft that considers that data and introduces gravity simulation technologies IE habitat wheels and space bolos space craft that rotate to generate a centrifuge effect as uniformly as possible. That that brings another issue larger ships.
Still a long winding road, although the US lost its own manned launch system with the shuttle its presence on the ISS has been continuous and they will be back under there own power shortly. The Russians have there own issues but are deeply linked to the CNSA successes having shared technologies and training.
I dont think China wants global domination as we know it from 19th and 20th century. China will probably dominate Asia. As a matter of fact it only needs to dominate Asia and secure key trade lifelines to dominate rest of the world.
Back to space race:
I believe china should have been invited to ISS by the US. You see this everywhere, when China is excluded from something it finds alternatives and even make their own. AIIB comes to my mind.
I still wonder what other utility there is for CZ-9 than moon launches. It will probably be ready for launch by early 2030s. By then the CSS will celebrate 10 years in LEO. Developing such a huge rocket for a few lunar landing seem a little waste.
I imagine CZ-9 ultra heavy version launching 2nd generation CSS modules, equipment for permanent lunar bases. Maybe man mission to asteroid? I believe man will be landing on a asteroid before it sets foot on red planet. Or may be blasting off with contruction materials for a huge long duration spaceship for journeys back and forth to Mars.
IMO major microgravity-related problems will be solved by 2040-2050.