I thought it was mentioned somewhere, but in any event...it obviously was not on or disabled since the neighbors would have certainly heard an alarm and it would have awakened the family. They would have all been up and probably not all found in the bedrooms, imo.
The fact the window was either unlocked or left open is important, but may not have anything to do with the murders. The screen could have been damaged before the murders and the window (if open) could have been due to moisture in the basement or for other reasons (someone was careless not to lock it). I still believe it was staged and no one entered through the window. The screen will show if it was torn/cut from the inside or the outside which will be helpful to LE in determining if someone came in that way.
There should be signs of someone crawling in the window, too. Footprints outside on the ground or on the side of the house, possible fingerprints, lint or fiber from clothing, smudges on the glass, marks on the inside walls, etc.
Also...wouldn't there be dew or moisture on the person's shoes from the grass? Grass tends to stick to people's shoes when damp, too. They should have some very clear signs that someone walked across the yard and crawled in the window including photos of footprints on the grass itself with the morning moisture.