Normally I try to avoid pedantry, but since this thread is essentially encouraging it...
First, if a musician is "Anyone who composes, conducts, or performs music" then by definition a DJ (not counting the "playlist->shuffle button" type) then there are an awful lot of DJs who are musicians - Skrillex, Deadmau5, Minnesota, etc., because they compose. Not all DJs compose, of course, but still. Broad brushes. :EDIT: The focus for the "no" answers seem to be with people sampling other music, but that's ignoring a huge swath of DJs who create content from scratch. And like someone said earlier, lumping them all together is a bad faith way of arguing.
Second, it seems like the biggest hangup here is that "they don't play an instrument," which I guess is valid from a very myopic point of view. After all, people who play an instrument have dedicated years or decades learning to make music with their instrument. How dare some kid with a PC find a new way to make music, amiright?
Never mind that many of them have dedicated years or decades learning to make music with their computers - that means they're musicians, as far as I'm concerned. I've never once thought Trent Reznor wasn't a musician because a majority of the music he has created has almost entirely been composed, recorded, and produced digitally.
But hey, as long as he doesn't call himself "DJ NIN" or something, he's different.
Never mind that the bar for what a "real musician" actually is always happens to be just below whatever level the person commenting feels is appropriate. Sort of makes it seem like the definition of "musician" is pretty subjective and thus flawed.