Moto X Battery Question
This issue gets pretty clear by the second screenshot, which I will repeat here:


Battery usage (click image for larger variant)

Please pay attention to its lower half, just below the graph, and let me point out some details:


Mobile network signal: This bar has no black, which means the radio was on all the time. Further, the colors indicate a relatively weak signal (see my answer here for details), which most likely caused the device to permanently watch out for a "stronger signal source", powering up the radio for that, and consuming energy for this task.
Wi-Fi: again, a continuous bar, so WiFi was turned on the whole time, consuming energy again.
Interim result at this place: With all sync on (as it is by default), the device would also permanently synchronize your data (in intervals, of course) – contacts, calendars, etc.pp. – which again consumes battery.
Awake: This bar clearly shows your device was not in "permanent standby". You always find "blue spots" on it, even during your sleep period (which most likely is, where the Screen on graph is black but there are blue spots on the "Awake" graph – i.e. most of the "last third")
Charging: Continuous black, so no charger was connected. Guess where the juice had to come from then :)


Conclusion: Pretty normal behaviour, though I cannot speak precisely how much battery-use would be normal (that depends on too many factors unknown to me, as e.g. apps installed, sync intervals, "consumption specifications" of device components, and so on). If you feel it should last longer, consider switching to airplane mode at night (or turning at least WiFi off). There are even tools available which would automate this – some of them e.g. mentioned with my above linked answer.