Need advice on moving some ducting.

[juster]

Thanks for the video. It is a great way to illustrate a problem.
Yes this looks like intake fresh air. Since I did not see your whole furnace, just the duct work I am assuming that this air is just for fresh air for your house. (you and your family) and not for combustion.
Combustion air needs to treated differently in that it should not be ducted into the return air duct. It should have its own incoming air dropped down beside the furnace.

I did look through the regs you linked but did not go through every doc. In my area there are no regs regarding where to put fresh air. There are regs on where to put exhaust air. Cannot place closer than 6 feet to intake air. So if you have an existing exhaust air duct, I would not move your fresh air close to it. Pointing down, point up, flush mount will make no difference.
As for your question of you wanting to move the fresh air intake to another location under your kitchen. As long as there is no exhaust air close by then no problem.
Just for the sake of knowing, did you ask the contractor why they put the duct where they put it. Maybe it was just a shorter distance and they could do the job quicker. It would be interesting for you to find out.

[juster]

I am assuming that you have a gas furnace when I referred to combustion air. If it is electric or a heat pump then do not worry about combustion air. Having the fresh air coming into your house at the duct work in it's present location is good enough. Still make sure that you do not have any combustion air exhaust from other gas appliances close to the intake air, if you have them.