I would argue that mutual intelligibility between Chinese speakers 2200 years apart would be essentially nothing, for the spoken language. I say 2200 years as the emperor in the film is the Dragon Emperor, or Qin Shi Huang, who lived 259 to 210 BC and founded the Qin dynasty.
To give you an idea, Old Chinese (~1250 BC to 25 AD) did not have tones (Old Chinese), while tones are as important as vowels to communicate meaning in Modern Chinese (Importance of Tones). Also, many of the modern varieties of Chinese are mutually unintelligible (Varieties of Chinese), and speakers 2200 years apart have to deal with both the language changes over time and the likelihood that they would not be speaking the same variety of Chinese. See this link for more information on sound changes overtime for Chinese. We also have not been able to properly reconstruct the sounds of Old Chinese, so even someone very educated in Old Chinese may not be able to understand a native speaker of Old Chinese without significant barriers.
Another interesting question is, if the spoken language could not be understood, what about the written language?
The biggest barrier along this route would be whether the person from 2200 years ago was even literate. If it is a randomly chosen person, they were probably not literate and thus there could be no written communication whatsoever.
The second barrier would be whether the modern person was literate. The literacy rate in China in 1949 was less than 20% (The Chinese Struggle for Literacy), so this may be a problem in and of itself.
If both the ancient person and the modern person were literate, I would agree with Tang Ho that written communication may be possible. I would also argue, though, that it would still be difficult and there may not be many modern people who would have the knowledge to be able to pull this off in the 1940s, unless they were highly educated. The first barrier would be the script. Chinese characters had various scripts in use over time, and they are very different from the modern script (see this example from Wikipedia). The Qin dynasty did have a standardized seal script (Seal Script) that is known today, but I have heard that Modern Chinese native speakers today have a hard time reading seal script (though a larger fraction of literate people may have been able to read seal script in the 1940s). So, unless the modern person from the 40s was both literate and educated well-enough to be able to read the seal script, they would have a hard time reading whatever the ancient person wrote. Other barriers include the very different grammar of Old Chinese to Modern Chinese, various variants of characters, and the changes in the meanings of characters over time. These are not insurmountable barriers, given sufficient education (and given what I believe was the knowledge level in the 1940s), but still difficult as a whole, I would say.
Granted, if the person encountered the Dragon Emperor because they were a high-level member of an archaeological dig/society that was seeking to revive the Emperor (as I think occurred in the movie), I could easily see that they would have sufficient education to figure out the writing of the Emperor. This is assuming that the Dragon Emperor was literate, which I presume would be the case for the Emperor of the Qin dynasty. Given enough time, and assuming that the Emperor was patient enough and willing to teach, a person from the "Revive the Dragon Emperor" society could maybe eventually figure out how to speak Old Chinese with the Emperor. I am not sure that this would be possible in the time frame shown in the movie, however.