Watching the video, it appears that the engine is not getting any fuel. I hear it sucking through the car as if it is straining for gas, but not getting any. Just for fun, while running, try closing the choke enough so it does not stall, then open the carb and see what it does.
Look down inside the carb with a flashlight (engine off/not running) and look at the primary side. Open up the throttle like you were flooring the car. You should see a nice stream of gas shooting into the carb, one stream of gas shooting into each barrel. If you accelerator pump is not doing its job, you won't see this stream of gas and this is what causes a richening of the carb when you stomp on the gas as the primaries open up. If you don't get that stream of gas, it will act as your video, fight to pick up RPM's, and stall.
You had the carb rebuilt, but the float could be set wrong and not allowing enough gas to fill the bowl. Have you adjusted your idle screws in the front of the carb? Screw them in gently until the stop - do not force these or over tighten. Then back them each out about 5 turns and see if that improves anything.
Next, have you checked your timing? Sometimes timing can be off and cause poor idle/running problems as well. This is the easiest thing to check first.
Finally, you may have taken a slug of water in that gas. The ethanol laced gas can do this and water can accumulate in the tank if it has simply been sitting around. You may want to unhook the fuel pump line at the tank side and run a length of rubber hose into a fresh can of gas to ensure you just don't have some crappy gas running through the carb.
And as pjw stated, look for any vacuum leaks. It is important to use the correct gasket for the intake/carb on the '67. This is off of a Chevy site, but applies to the 1967 intake manifold/Q-jet and explains what I am talking about. Q-Jet Carb Base Gasket Tech Info: The "Hot Slot" Manifold Problem - CorvetteForum - Chevrolet Corvette Forum Discussion