Why is some application not supported by device with Intel processor Pokemon Go is releasing today but sadly I saw somewhere in the Internet stating that Niantic has claimed that the app is not supported by devices with intel processor (in my case asus zenfone 5). So I wonder why the type of processor will be one of the factors determining whether the app is compatible for the device. Any help is appreciated. =)
Note: This answer covers other apps than Pokémon Go, as Pokémon Go has been updated to work with x86 processors

Apps contain multiple architecture dependent and architecture independent parts:


Independent:


Dalvik code
Android resources
the Manifest

Dependent:


Libraries
Special assembly code in the Dalvik executable (rare but possible)



The major things are the libraries.
Those are shared objects (.so files) much like DLLs on Windows that contain bytecode.
They are compiled using the Android NDK (Native Development Kit) and are compiled for a specific architecture (like compiling Linux applications using a cross-compiler, ie. compile ARM code on an x86 machine).
In our example, this library can only be used in an ARM environment were the ARM bytecode is understood.  

Some Android x86 devices (commercial phones/tablets, not the emulators) come with a special ARM Translation toolkit, aka. libhoudini. It basically translates ARM instructions to x86 instructions.
Those instructions however, are not optimized to run on x86 hardware and thus result in poor performance and high battery usage (the latter of those is one reason x86 is not primarily used in mobile processors).

The real problems are the developers:
Either:


They do not compile their libraries (often containing proprietary code) for any other architecture, for some reason.
They use specialized bytecode, only available on ARM so that any ARM Translator or libhoudini fails.


Luckily Pokémon Go received an update, allowing users of x86 devices to run the app, but other apps (mostly games) do require a real ARM device.