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The Moto X4 doesn't explicitly claim to support USB Power Delivery based charging, but when you connect it with the third party Verizon USB Type-C Wall Charger with Fast Charge Technology, the phone appears to charge using USB Power Delivery through Lenovo's TurboPower branded technology as seen from the Granite River Labs GRL-USB-PD-A1 power analyzer.

When connected over USB Type-C, the Verizon USB Type-C Wall Charger with Fast Charge Technology first advertises over USB Power Delivery to repeatedly offer the following power profiles- 15 watts (5 volts @ 3 amps), 21 watts (7 volts @ 3 amps), 24 watts (8 volts @ 3 amps), 24 watts (9 volts @ 2.7 amps), and 24 watts (12 volts @ 2 amps) to the Moto X4 on a fully drained battery.

When Verizon again displays the same source capabilities after a hard reset, only does the Moto X4 starts to request 15 watts (5 volts @ 3 amps) which is accepted by the charger. Note that the hard reset happens as the phone is turned on. 

We then observe the Moto X4 repeats the initial 15W power contract but later decides to charge faster using a higher 24 watts (9 volts @ 2.7 amps) charging power which Verizon also agrees to provide.

A hard reset later, we can also see both the charger and phone cycle through the same initial power negotiation as earlier observed.

The power graph actually shows that upon initial plugin from zero charge, the Moto X4 starts off pulling around 1.6 amps when at 5.2 volts while the phone is switched off. As it boots up, power delivery negotiation begins during which the current pulled starts to fluctuate.

Over the first hard reset (where the phone turns on) and power requests, there’s a sudden drop in voltage with no current being pulled, but quickly resume after a while to reach about 14.8 watts (5.3 volts @ 2.8 amps) charging. As the 2nd power request is made, almost no current is being pulled while the voltage goes up to about 9.1 volts. The current then slowly picks up but yet again drops quickly to zero along with voltage as the initial power cycle gets repeated. The phone then continues to charge by drawing around 14.8 watts (5.3 volts @ 2.8 amps) as similarly observed in the initial stage of charging.  

While charging doesn’t go as smoothly, the Moto X4 can get up to almost 15W over USB Power Delivery with the Verizon USB Type-C Wall Charger with Fast Charge Technology, to charge as quickly as using its own TurboPower based charger that came with the phone (more details here).