Aiming to throw out the foreign invaders that one's corrupt and incompetent government was defeated by is both 1) indeed an example of dissatisfaction with internal systemic problems and 2) not the same as looking to catch up with the foreigners.Are you sure we talk about the same country?
Do you know that the Boxer "rebellion" target was to support the central government, and to get rid of the foreigners (Europeans)?
Before 1600/1700 China was THE civilised country on the Earth, they didn't cared too much outside of the kingdom.
At 1850 Europe become as powerful as China, and by 1900 the political class of China recognised that the advantage of the Europeans method is not simply a temporal thing , like the mongols, but a exponentially growing gap between the capability of the imperial china and the capability of any European country.
The Chinese become dissatisfied due to that, the elite wasn't capable to protect them and they lifestyle.
By 1900 the Europeans (And Japanese who was faster to copy part of the European methods) had full freedom of action in the Empire, and the Imperial army was not capable to defend the area of China.
Mao get the support to do whatever he see as necessary to close the gap between China and the Europeans due to this.
There is a reason why the Chinese(and before Japanese) learn European science, the methods developed by Germans, British,French , Swiss etc. scientist.
In China they teach Newton-Leibniz, Maxwell, and so on.
The interesting is these technical methods are the results of the legal / corporate system, not the reason of them. : D
So by simply copy them technology the Chinese making the same mistake like the Soviets.
Military technology, other scientific knowledge and methods, and various socio-economic systems are all tools/"technology" China has been learning, using, adapting and developing further which have all served it well enough because the drive is self-improvement.
Self-improvement is inherently open-ended in absolute terms, within the more limited scope of relative terms it is "catching up" while others are better off but that is just a "side effect" or secondary effect that may be achieved then superseded along the way.