USB-C DisplayPort Alt Mode
USB-C Alt Modes allow for signals other than USB to be carried on the pins of the USB-C connector. In particular, DisplayPort Alt Mode specifies how a DisplayPort signal is carried.
At its most basic, the Type-C connector becomes just a weird DisplayPort connector that uses several of the pins for DisplayPort signaling. This Anand Tech article has a nice diagram showing how the pins of the type-C connector are reallocated from use for high speed USB to being used for DisplayPort. In particular, the SBU1 and SBU2 pins are assigned to carry the DP-AUX channel. I2C communication, used by DDC/CI, is (one of several) signals that can be "multiplexed" on the AUX channel. So a Type-C output from a host to a Type-C input on the monitor, or a Type-C output from a host to a DP input on the monitor should just work.
A Type-C connector cannot implement DisplayPort Dual Mode. It can only emit a DisplayPort signal, not a TDMS DVI or TDMS HDMI signal. To communicate with a DVI or HDMI monitor input, an Active, not a Passive, adapter is required somewhere in the chain of cables and adapters from the host device to the monitor. Note that a Type-C to HDMI connector of some sort, such as a simple dongle or a docking station, will perform Active signal conversion.
In all tested cases, if a Type-C to monitor connection displays a video signal, the I2C connection required by DDC/CI, works,