Please understand that the monicker "tablet" can be applied to any hardware using any operating system. The Google Play store is restricted to the Android operating system. Therefore, only tablets that run Android OS will have access to the Google Play store, and even half of those tablets won't receive authentication from Google so they won't have access to the Google Play store either.
Since the Asus VivoTab Smart runs Windows 8 as its operating system, it cannot natively support access to the Google Play store. You can virtually run an Android OS using a program called BlueStack, but you are merely mimicking an Android OS and will run into hardware and driver errors.
Windows 8 has its own app store. That will be the native app store that you will use for this tablet, although calling it an "app store" is silly since it's similar to purchasing software off of Amazon or from your local Best Buy and installing it on the computer. An "app" in Windows can be called a traditional "program". Lenovo has their own app store for Windows operating systems, so you may be able to side-load those apps. If Asus owns their own app store, then you will be able to access their apps. Google offers an app store for Google Chrome; therefore, if you install the Google Chrome browser, you will have access to the Google Chrome app store.
However, you will not be able to load apps from the Google Play or the iPhone/iPod/iPad app store.