According to the official Asus ZenFone AR specs, the phone's screen has 60ms touch response time, which is mostly important when playing games where you want the screen to quickly response to register touch events as fast as possible and this vary between different screens.
I never heart about any phone manufacturer mentioning the term 'touch responsive time'. Googling it, I came across and article on phonearena.com, that talks about a an app that called TouchMarks that benchmark the device touch response time. The article is from 2013, but you can see that the iPhone 5 back then had the fastest response time of 55mm, while many other phone trailes begind with HTC One with 121ms, Moto X with 123ms and Galaxy S4 with 114ms.
In this page on xda-developers.com, the poster mentioned some response time for more devices, and we can clearly see that for many new phones that touch response time is significantly improved. HTC One M8 has 46ms, LG G3 50ms, iPhone 6 65ms, etc.
I can tell you from my own experience, that I remember that there was always a lag in Android phones when I dragged icons, whether on my iPhone 5S it was much more responsive. So 60ms is relatively very fast and stand with the industrial-leading claimed by Asus on the official Asus ZenFone AR specification page.
Of course a fast touch responsive time is very important for gaming, and especially for this specific phone that can run Google Tango augmented reality games on it - Definitely a worth mentioning advantage.