Sadly there are many reasons for ping to fail. We have firewalls (even in the router), the OS settings and a feature that has MANY NAMES. I'll give it one and leave it to you to find what your router calls it. The name is CLIENT ISOLATION. I decline to write down the other hundred names I've seen this by.

But what is DIFFERENT about your post is "The work laptop is on a domain." This can mean that it's on a VPN and it would be absolutely proper to not be able to ping machines that are not on the DOMAIN. Your IT staffer should explain this but it is proper.