When the Play Station 4 was released it was also announced that there would be a remote play feature which would allow you to play your Play Station 4 remotely from your Xperia Z3. A Sony representative had also said that Sony did not plan to bring this feature to any other device. No worries the dev community has come through again. Developer "XperiaPlaystation" has ported Remote play to all android devices. To make this work you will need to flash a particular zip file and install a certain apk. Your device must be running Android 4.0 or better. You will need to have a custom recovery installed like Clock Work Mod recovery. Head to the link below for the downloads.
Via XDA