Our hotel is not listed above. However, can we still get a free shuttle going to Kowloon?

First of all, you may misunderstand the free shuttle buses, which cab be only taken at Kowloon Station or HK Station after getting off from the Airport Express Train.
Actually, as long as you get off at Kowloon Station by Airport Express, you can catch the free shuttle bus of the hotel to reach there conveniently.