I think it's not just a love song, it's a song about "online love". That's why it's called "digital love" and why the last line says "Why don't you play the game?". So he fell in love with a girl he just knows from online-gaming (and it seems like there will never be more, maybe she already has someone or is too old or whatever), waiting for her to log in again, so he can spend some more time with her.
Just something I wanted to add:
I think it's not just a love song, it's a song about "online love". That's why it's called "digital love" and why the last line says "Why don't you play the game?". So he fell in love with a girl he just knows from online-gaming (and it seems like there will never be more, maybe she already has someone or is too old or whatever), waiting for her to log in again, so he can spend some more time with her.