Agree with CRobGauth that the definition of "mobile device or tablet" when used in this context means a device capable of running the mobile app (i.e. a smart phone or table). That definition is not unique to Verizon as I've seen it used similarly in other senarios.
The key is being able to run the "app". Your laptop, while mobile, can't run the app. Same would apply to an old or off-brand phone which couldn't run the "app".
What would be interesting, although off topic a bit, would be if some of the newer models of Smart TV's that can run apps from one of the mobile application stores would look like a "mobile" device and work.