In Dalton's law all gases are assumed to be ideal gases that have no interactions with themselves or other gas particles. Each gas produces its own individual pressure independently of any other gas. The individual pressures add up to a total pressure. Each gas pressure is dependent on the number of particles of that gas or said another way the number of moles. The number of moles of a gas divided by the total number of moles of all the gases is called the mole fraction. Multiplying the mole fraction of any one gas times the total gas pressure will give you the individual gas pressure from the one gas. This is because each gas occupies the whole volume available (all gases then have the same volume) and they have the same temperature, so their pressure is due to the number of particles. In the video you could get the 78.1 kpa for nitrogen by subtracting off all the other gas pressures from the total pressure of 101.3 kpa.