According to that description, this is a genuine Thunderbolt-3 Display (similar LG display sold outside the Mac App Store is only a USB display).
USB-C is the name of the connector, ONLY. It does not describe any function of the cable.
To be effective, the cable should have the ThunderBolt symbol on each end, not a USB symbol. I would expect this display to work ONLY with the Apple Thunderbolt-3 to Thunderbolt-2 adapter used with a cable that carries the Thunderbolt symbol on each end. No others, such as the Apple MacBook Charging cable (which is useless for anything but charging) will work.
But be sure to do a Restart or sleep-and-wake your Mac to be certain the display is recognized (if possible). If that does not work, then they have indeed sold you stuff that will not work with your Mac.
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Best results for other displays are provided by displays with modern DisplayPort family interfaces. These display drop the "heartbeat" refresh required for CRT displays and send only the changed data. The lower data rate means everything runs cooler. A screen buffer in the display itself keeps refresh rates as high as possible. The Dell you mentioned has a [Full Size] DisplayPort interface, accessible with a cheap Mini DisplayPort (plugs directly into ThunderBolt-2 ports on your Mac Pro 2013) to [Full Size] DisplayPort adapter cable.