There is already plenty of this on a daily basis for a number of reasons.

Although the games may help I am skeptical of what it would accomplish in the long run besides exposing more foreigners to China on a pretty superficial basis (though that's far better than nothing). The Chinese traditionally do not trust foreigners (IME neither do the Japanese or Koreans FWIW). Unfortunately, it goes both ways in that no one (foreign) really trusts them (The Chinese) either. Trust and friendship in China takes a while to cultivate, much longer than in the west, but once it's been done you're friends for life and people will go out of their way to do all kinds of things for you (of course the same is expected of you).