Moto factory firmware images are flashed with fastboot, not recovery, so you need to do some homework/setup first. Be aware that downgrading a Moto device, while sometimes possible, is NOT supported and can result in a bricked device. You must use a factory image that is the same or newer version than you have installed already.
** BACKUP ANY IMPORTANT DATA - EVERYTHING WILL BE LOST **
** Enable OEM Unlocking in Developer Settings PRIOR to starting **
Backup is self explanatory. By enabling OEM Unlocking you are giving yourself an out, if something goes really wrong you have the option of unlocking the bootloader to correct it which is not possible if this switch is not set prior to starting.
If you are using Windows, you will need to install the proper drivers (Google can help you with this, I use Linux so drivers for Android devices are not relevant). Then you will need fastboot on your computer, you can get it from Google as part of the Android Studio package, Minimal ADB and Fastboot package, or if using Linux it is part of most distrobution's repositories.
Next extract the ZIP you linked above to your fastboot directory and shut down your phone. Startup your phone while holding the VOL DOWN button, you should get to the bootloader screen (if not, try again), then connect the USB cable and open a terminal or command window and enter the command:
If you get a response similar to "List of devices: SomeLongString fastboot" you are ready to begin the flashing process. Enter each command individually ONE AT A TIME and verify each step results in a result of "Okay", if any step fails repeat it up to 2 additional times (modems frequently do not take the first time)
fastboot oem fb_mode_set
fastboot flash partition gpt.bin
fastboot flash logo logo.bin
fastboot flash boot boot.img
fastboot flash recovery recovery.img
fastboot flash system system.img_sparsechunk.0
fastboot flash system system.img_sparsechunk.1
fastboot flash system system.img_sparsechunk.2
fastboot flash system system.img_sparsechunk.3
fastboot flash system system.img_sparsechunk.4
fastboot flash system system.img_sparsechunk.5
fastboot flash modem NON-HLOS.bin
fastboot erase modemst1
fastboot erase modemst2
fastboot flash fsg fsg.mbn
fastboot erase carrier
fastboot erase cache
fastboot erase userdata
fastboot oem fb_mode_clear
(Every recent Moto Android device uses this same process, it is derived from the contents of flashfile.xml that is contained within the factory firmware image itself and used by Moto's factory flashing tool)
The first boot may take a significant amount of time, 10-20 minutes even, just let it work and do not interrupt it.
Be aware that there additional resources for this on XDA in their Moto E 2015 General Discussion area, including threads specifically for firmware images and flashing instructions.