How can I open this locked window?

Following the comments, the thing to know is that the lock itself is only keeping the handle from rotating, so it doesn't matter at all if you rip the barrel out (other than cosmetics). The handle will still actuate the latch, which is how it holds the window securely closed.

If, as Duston suggested, you can pop that cover & remove the entire casing and handle, then you can probably remove the actual locking mech without removing or damaging the key entryway (the little silverish bit). That's the ideal solution.

Worst case, if something critical snaps in two, take the remains to $BIG_HOME_IMPROVEMENT_STORE of your choice, and buy one to match. Shouldn't be very expensive.

I have opened a similar broken handle. Gently wiggle a thin piece of steel, e.g. stanley blade, between the rotating handle and the fixed base, below the black part of the button. There should be a sprung plastic catch that can be pushed up towards the button and then the handle should turn.

Check your other working lock first. When it is open you should be able to feel the catch.

There are usually two screws holding the handle in place. One under the gold cover on the left and one under the handle when it is open. This is a common window handle and should be easy to find replacements from online stores or local window fitters.