China unveils video of its moon base plans, which includes a NASA space shuttle

Enough of the plans of the Shuttle were public that the Soviets had managed to build an improved copy (https://en.wikipedia.org//wiki/Buran_(spacecraft)?&useskin=v...), so it wouldn't really be theft if China did the same thing with the Shuttle, but it's funny because launching a Shuttle off the Moon is nonsensical, as is the scale of all the other structures they show.

To more clearly answer your question though, besides the fairly strict ITAR controls for certain parts, the main barrier to acquiring space tech is materials, which is more of a challenge to steal since a lot of it depends on experience rather than documentation. Eg SpaceX can openly show its Raptor engines and what part does what (besides the injector design, which is ITAR protected), because the challenge isn't knowing how a Raptor works, it's knowing how to make and work with the alloys used and how to control the resulting engine.

The external appearance of a rocket is the easy part, so something looking similar is not evidence of theft.

No real need for marketing as project funding is set by bureaucrats and engineers.