Yes you can rent some movies, the HK store has been changed. For MLB, it is subscription based to open to the whole world so should be good, I have seen highlight from AppleTV3, loads very fast. However, you should expect the performance to be different if you watch live games.
To be honest for most people in HK, I don't think online movie streaming rental will be of much interest, unless may be you are caught in a typhoon and don't want to leave home.