I think we're going to need more context, since I can't find the song with Google.
It is most-likely a play on "typing in" and "hanging out".
"Typing the words in" means to just "type the words into a particular area".
I am now typing these words into a window, and they will be posted on WR forums.
Type the words in the box, and then hit "enter".
"Feels like hanging out" most-likely means "feels like I am telling you everything about me".
So the sense of the whole sentence is:
Typing/writing these words to you, makes me feel like I am telling you everything about me.
Perhaps something like:
Se scrivo queste parole, pare che ti/vi dico tutti di me.