In japanese, we often use no subject( I, he, she, you) in the beginning of a sentence.
Of cause you could start a sentence from a subject; however, it sounds a little bit strange in a conversational language.
It more sounds like it is spoken by a foreigner for me.
Anyway, "I like playing games".
1. ゲームするのが好きです [ge-mu surunoga sukidesu.] (I like playing games)
-ゲーム(game) する(play) のが(to/ing) 好き(like) です(is/am/are ...etc)
2. ゲームするの好き [ge-mu suruno suki]
(short of #1, more used in conversational language)
-ゲーム(game)する(play) のto/ing) 好き(like)
3. ゲームが好き [ge-mu ga suki] (I like games)
- ゲーム(game)が 好き(like)