There's also the matter of latitude. The Atacama is on the Tropic of Capricorn, so it'd probably be desert even without any mountains. It's just a (to use a cliche so inapt, I must use it when I'd normally avoid it) perfect storm of desert-producing conditions that makes it "the driest place on Earth". Rain shadows are important, but they aren't the only thing. If the wind is going west to east, I agree with bartmoss on placing the desert (although then what is desert here may still be pretty dry unless it gets rain coming up from the south or maybe the northwest, across that big lake), but if it is east to west, the other mountains appear small and unlikely to have a significant rain shadow effect. The northern mountains look like they'd block a lot of weather and that could keep climates more mild if this is in the northern hemisphere.