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.
Bob