Communications between such a thingamajig capture card and a laptop has nothing to do with DP Alt mode or USB HID, it's whatever custom USB packet types that capture card manufacturer comes up with. That technically wouldn't be an answer to your original comment in strict sense.
The most likely heuristic paraphrasing for your original query is something like "are there ways to multiplex DP _source_ and HID _peripheral_ on a single USB3+DP Alt connection". That made no sense at multiple levels on top of being unlikely to be possible. That lead to people hallucinating wildly.
The alternate question "are there ways to plug an SBC into laptop somehow for remote control, over a single USB-C cable" has that dongle as an answer as we now know in hindsight. But that is not a straightforward interpretation and response for your original comment, especially with your follow-up replies about DP Alt mode specs that would not be used by such a device.