A developer (TheScriptKitty) over at the xda-developers forum has released a port of the PS4 Remote Play feature and app that works on any non-Xperia Android smartphone or tablet. It can easily be installed on any device, be it rooted or non-rooted. However if you want to use a Dual Shock controller you will require root access as well as a few extra steps during the installation.

Want to use your Android device for PS4 Remote Play?

Seeing as the official PS4 Remote Play app only supports Xperia devices, this little app port might be quite appreciated. It appears to have been recently updated to better support Dual Shock 4 Controllers. As mentioned, for Dual Shock controller support, you will need to have a rooted device and preferably some technical know-how. Below you will find the requirements and step by step instructions as per the original forum thread over at xda-developers, as well as a video tutorial.

Requirements:

• Android 2.2 and above running on a smartphone or tablet.
• Root access (optional).
• Custom recovery installed (optional).
• Remote Play Port APK from here.

Non-Root Method (without Dual Shock Controller support)

1. No root access required, just download the Remote Play Port APK file and side-load it on your phone or tablet.
2. Done!

Root Method (With Dual Shock Controller support)

1. Download RemotePlayInstallerV0.7.4.zip or RemotePlayInstallerMinimalV0.7.4.zip
2. Enter Custom Recovery, Flash ZIP and Reboot.
3. Install PlayStation App from Play Store(Optional).
4. Download and Install Sixaxis Controller App(Optional)
   1. Pair the controller via USB to your PC using the supplied program on Dancing Pixel Studios website. (You will enter the Mac Address found at the bottom of the app).
5. Done!

Manual Method

1. Download the ZIP and extract it.
2. Open up File Manager of your choice, Copy/Move the DualShockManager.apk you just downloaded into the '/system/app/ '(For Lollipop Create a folder named: DualShockManager in '/system/app/' and copy it their) Directory on your phone, change the Permission of that .apk to RW-R-R(Optional).
3. Move/Copy data@app@com.playstation.remoteplay-1.apk@classes.dex, data@sdext2@com.playstation.remoteplay-1.apk@classes.dex and system@app@DualShockManager.apk@classes.dex to the '/data/dalvik-cache/'('/data/dalvik-cache/arm/' for Lollipop) Directory. Same as above you need to change permissions to RW-R-R(Optional).
4. Move/copy com.playstation.remoteplayident.xml and com.playstation.playstationcertified.xml to the '/system/etc/permissions/ ' Directory. Once again, change the permissions to... RW-R-R(Optional).
5. Okay, now for the important files, .jar's, if you know java lol. File one, File Two
6. Move/Copy com.playstation.playstationcertified.jar and com.playstation.remoteplayident.jar to the '/system/framework/ ' Directory. After they have been successfully copied them, change the permissions to RW-R-R(Optional).
7. Now, Reboot(Optional)!
8. Install the Remote Play App.
9. Go to Play Store and download PlayStation App(Optional).
10. Done!

[youtube http://www.youtube.com/watch?v=gKljWdljk_A]

I highly suggest you check out the forum thread, especially if you have any questions or need to troubleshoot the installation.