Is my furnace vent installed correctly
The other intake pipe appears to be capped. With no direct air inlet and the old line capped this sets up problems including code compliance issues.
I would verify with a local building code inspector, I don’t do furnaces full time but that would not pass inspection in my jurisdiction, to me it looks like a lazy installer trying to save a buck.
So my answer is NO it is not right. it should have a fresh air source.