Hi there!
It sounds like you're looking for a new tilt latch. Before I recommend anything, can you write out the distance between the two installation holes, measured from center-to-center? That will help us narrow down your options.
Thanks! Based on your dimensions, I think our 26-120 and 26-121 are the best options for your original tilt latch. The dimensions match up precisely, and the design is very similar, as well. Look it over and see what you think.
I also just realized that your window is a horizontal sliding window; I apologize for not understanding that before, I didn't notice how your backyard was oriented in your first photo. It bears mentioning that these latches are made exclusively for double hung vertical windows. They are not really meant to work on horizontal units like yours.
Based on this, and the design of the lock (which is also not something you see on horizontal windows), I suspect that you actually have a vertical window that was installed sideways. Just something to keep in mind. You may want to consider replacing the window at some point in the future so that it will function properly. I can't imagine that what you have here is easy to slide.