I think you're just getting hung up on the variable name $clients. Ikegami's first code block is showing you the basic strategy of an event-driven program as applied to sockets. At the most conceptual level, it's something like:

while application doesn't need to quit:
    does task 1 need attention?
        Yes?  Give it a little lovin'
    does task 2 want a hug?
        Yup--give it a bear hug
    . . .
    is task n unhappy?
        Uh huh: Give it a smile
[download]

The rules are that (1) asking a task whether it needs attention can't take a long time--otherwise you'll starve all your other tasks; and (2) none of the tasks you're performing can take a long time, either, for the same reason. So you'll use non-blocking I/O techniques to check your sockets because a normal read without checking will wait until that socket has something to say.