1. He is good at playing billiards.

2. He is good in playing the billiards.
(Can we use 'in' instead of 'at'?)

3. It's the first play-off game, and I'll be the catcher.

(What is the meaning of 'the first play-off game'?)

4. I am disappointed because this is a very important game for me.

5. I am disappointed because this is a very important game to me.

(Can we use both 'for' and 'to' in the sentences above?)

1 answer

1 is correct; 2 is incorrect. (Don't use "in" in this situation.)

3 is correct. A play-off game is part of a series of games after the regular season is over; these games are played to determine who will be first in the whole league or district. Here are several websites about the basketball playoffs going on in the US right now:
http://www.google.com/search?q=nba+playoffs&rls=com.microsoft:en-us:IE-SearchBox&ie=UTF-8&oe=UTF-8&sourceid=ie7&rlz=1I7GGIE_en

4 and 5 are both correct; 5 is probably used more often.