Answer:
Yes, the character in the video commits metaphorical suicide. Please note, that this is just a music video and the events did not really happen. The character is using this metaphor as a way of expressing his pain, and is not endorsing the action.
If you have serious suicidal thoughts, please get counseling.
"You're so in love with this woman and you don't understand, 'What am I doing wrong? What am I not giving to you? I'll go as far as putting as putting a bullet in my brain for you, and why can't I get that kind of love in return?'"
---Bruno Mars on writing and the meaning of "Grenade"
See the discussion board for further discussion about this video.