The newer model 9370 has no USB Type-A ports, but does have two USB-C/Thunderbolt-3 ports, at least one of which has 4-Lanes, and can use the WD15 to drive a single 4K monitor at 60Hz. or a pair of WQXGA (2560x1600) displays at 60Hz
I'm not so sure on that anymore -- the WD15 "manual" claims it can do the above with a 4-lane connection, but everything else from Dell says No!
Somebody with a 9370 is going to have to just try it. Linux reports thusly:
$ lspci -tv
-[0000:00]-+-00.0 Intel Corporation Xeon E3-1200 v6/7th Gen Core Processor Host Bridge/DRAM Registers
+-02.0 Intel Corporation UHD Graphics 620
+-04.0 Intel Corporation Skylake Processor Thermal Subsystem
+-14.0 Intel Corporation Sunrise Point-LP USB 3.0 xHCI Controller
+-14.2 Intel Corporation Sunrise Point-LP Thermal subsystem
+-15.0 Intel Corporation Sunrise Point-LP Serial IO I2C Controller #0
+-15.1 Intel Corporation Sunrise Point-LP Serial IO I2C Controller #1
+-16.0 Intel Corporation Sunrise Point-LP CSME HECI #1
+-1c.0-[01-39]----00.0-[02-39]--+-00.0-[03]--
| +-01.0-[04-38]--
| \-02.0-[39]----00.0 Intel Corporation DSL6340 USB 3.1 Controller [Alpine Ridge]
+-1c.4-[3a]----00.0 Qualcomm Atheros QCA6174 802.11ac Wireless Network Adapter
+-1c.5-[3b]----00.0 Realtek Semiconductor Co., Ltd. RTS525A PCI Express Card Reader
+-1d.0-[3c]----00.0 Samsung Electronics Co Ltd Device a808
+-1f.0 Intel Corporation Device 9d4e
+-1f.2 Intel Corporation Sunrise Point-LP PMC
+-1f.3 Intel Corporation Sunrise Point-LP HD Audio
\-1f.4 Intel Corporation Sunrise Point-LP SMBus
pci 0000:01:00.0: 15.752 Gb/s available PCIe bandwidth, limited by 8 GT/s x2 link at 0000:00:1c.0 (capable of 31.504 Gb/s with 8 GT/s x4 link)
pci 0000:39:00.0: 8.000 Gb/s available PCIe bandwidth, limited by 2.5 GT/s x4 link at 0000:02:02.0 (capable of 31.504 Gb/s with 8 GT/s x4 link)
The first "limited" line (above) is for the dock as a whole.
EDIT: The second "limited" line is regarding the [s]USB3 hub ThunderBolt USB3 host controller within the dock, used for the USB3 Type-A ports as well as the integrated USB-ethernet adapter. The presence of a ThunderBolt USB host controller there is strong evidence that this is actually a ThunderBird3 dock.[/s]
EDIT3: Ah.. This could actually all be referring to stuff inside the 9360 itself, not the dock. I just did an experiment: unplug the dock, and notice all of the ThunderBolt devices vanish. Then, plug in a USB hub to the USB-C port on the notebook, and .. presto! All of the ThunderBolt devices, including the USB 3.1 host controller reappear.
So.. still no idea what is actually inside the WD15 itself.