Are we doing kirtan to the sangat or to the Guru?
I believe it's both. Some ragis will say they do it for the Guru and don't care about the sangat. But the ragi is the Guru's voice. The raagi is conveying the Guru's words to the sangat. Its a huge repsonsibility. For most of the divan the sangat is going to hear the Guru's word through you.
Guru Nanak used to ask Mardana to play the Rabab. As the Bani came to Guru ji he had Mardana play music. Guru Nanak was the vehicle to bring that Bani. There are some stories where Guru just asked Mardana to play music. So we can conceive that Guru Nanak used to just listen to the music for enjoyment. Similarly, when we play kirtan the Guru wants to hear it.
So I believe that when we play for the sangat its a huge responsibility. We also play for the Guru to enjoy it.