As suggested in this Reddit thread, the fun part is the randomness of Darryl finding amusement in a kids show, and especially the guy behind the camera.
Additionally, here it is implied that, since Freddie (the friend with the video camera) reached puberty during the show, his voice could have been amusing to Darryl.
A little background information of the scene from a conversation with Mindy Kaling sheds a little more light on that scene:
I have a two-part question: a) are you or one of the other
writers a fan of iCarly? and b) what made you choose Freddie (the
friend with the camera) as the part Darryl would enjoy the most? Loved
the random humor of that!
Thank God for the Dads on the show. I have not seen iCarly.
That was a pitch of some brilliant Dad writer.
B.J. however pitched the unaired last line of that Darryl Talking
Head, which got cut for time, which broke my heart. The line was
supposed to go: "That kid with the video camera? He’s got a nice way
of talking." (Then, dead serious) "The Suite Life I cannot do."