What was happening when the guy poured liquid gasoline into the manifold was that a very small amount would have vaporised. When it dripped into the cylinder a little more would have vaporised. When he started cranking the engine a little more would have vaporised. But you notice it took quite a lot of cranking to get it to fire and it ran pretty roughly. Once it had fired and misfired a few times there was enough heat to get it running reasonably smoothly, but it probably would not have held any load, because the fuel cannot vaporise fast enough to get sufficient vapor burning to provide the energy to hold the load.
When running as designed, the carburetor jets in conjunction with the intake manifold and combustion chamber , break the fuel into very small droplets, such that they have a very large surface area in proportion to their total mass and thus can evaporate very quickly and sustain higher powers.
Even inside the engine they are not fully vaporsied when combustion starts, but they first start burning just at the surface (actually just off the surface) of the droplets and then extra heat accelerates the process . (We are talking small sizes and time intervals here).
You can verify your self that the vapour, not the liquid is burning by pouring some gasoline into a metal bottle top lid , putting it in a place with no wind and hold a match at the surface to get a flame going. If you look very carefully from the side, you will see that the flame actually starts a few millimeteres above the surface of the liquid.
So technically and scientifically you are correct , only gasoline vapour burns , not liquid.