Only incident I had like this was when my dad took off and was missing for about 7 hours (he's diabetic so my mom was worried like hell) she called the police for help, sent an officer here, and for whatever reason he searched all the rooms quickly.
Bad for me I was tinkering with few of my airsoft guns (just maintaining stuff) he looked closely for about a min and just moved on. I can't recall a moment in my life I was more scared.
Best wishes though to your family and your items
It doesn't make sense they took other things when pretty sure the warrent only would say "Xbox 360"