No, the VeriFace won't work on Asus laptops because this is an application that was developed especially for the Lenovo hardware. If you try to install it on an unsupported environment, an error saying that the platform is wrong will be shown instead. You have to check the downloads for your Asus laptop. On the download page, choose other operating systems to see available apps, instead of the one that is currently running on the device.
You can start with the official website: https://www.asus.com/support