I just got a CH32V003 development board. I loaded the board library for it and got Arduino to recognize the board and load an example. The board has a USB-C connector but the computer doesn't see the serial port and I can't find drivers for it.
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The CH32V003 does not have USB hardware, so many of the low-cost "development boards" for it are using USB only for power, and you'll need a separate USB/Serial converter to talk to the UART.
(There MIGHT be boards with the USB converter built-in, and you said you got a sketch to load...; exactly which board do you have?)
I suspect that "load" does not necessarily means "upload" 
That's correct, it was just loaded into the app not downloaded into the chip. Any ideas on the port recognition?
Waiting for: exactly which board do you have?
It probably doesn't HAVE a "port"; you'll have to add your own.
Do you have one of these, or a similar board with just ONE chip on it (i.e. the CH32 controller)?
If so, there will be no COM port detected by the computer as you plug this in. As suggested above by @westfw these boards have no UART to USB bridge. You'll have to use a separate bridge; e.g. one of the popular "FTDI cables".
OK, I kind of thought so. Thanks for the reply!
Just to clarify for other readers: to program the CH32V003 you need the WCH LinkE programmer. That programmer also includes a Serial to USB converter.
The V003 doesn't contain a bootloader and cannot be programmed over serial. The LinkE provides a single-wire debug interface that can be used for programming and also for debugging. Real time debugging works great on version 2.x of the Arduino IDE.
Note that when you use serial on the SOP8 model, this will reassign the SWIO programming pin. After programming the SOP8 for serial use, you need to use Power-off-erase the chip to regain the programming function of the SWIO pin.