Locked and not rooted Moto X stuck on the boot screen

Here is the situation :
I have a Moto X (1st generation), it's completely genuine, never been rooted or unlocked.
I was using Whatsapp and Airbnb apps, when suddenly a message pop up on the screen, it was like "The service com.google.IdontRememberWhat**** stopped". So I pressed the only option that was "OK", and this message instantly appeared again. Then there was a wild battle between my phone and I which consisted of an endless succession of pop-up/OK. My phone won, and I decided to turn it off which was the only thing I could do at that point.

Now, the situation is that my phone doesn't want to boot. When I start it, it stays 1-2 minutes on the boot screen with the Motorola logo, then it reboots. Endlessly. I accessed the bootloader by holding "power" and "Vol-".
The screen looks like this :

- If I try the option "Factory", the phone goes on its reboot-logo screen loop
- If I try the option "Recovery", I get this screen :

On this screen :
- If I try the option "wipe data/factory reset", the screen is stuck on
"-- Wiping data...
Formatting /data..."
for like 1 minute and the phone enters in its endless reboot-logo screen loop.
- If I try the option "wipe cache partition", the screen is stuck on
"-- Wiping cache...
Formatting /cache..."
for like 1 minute and the phone enters in its endless reboot-logo screen loop.

So, at this point what are my options apart from playing baseball with the phone ?

I see that in the recovery menu there are these two options "apply update from sdcard" and "apply update from ADB". Does anyone know if I can save my phone with these options (taking into account that my phone is locked and not rooted) ? And how ?

Thanks