What the guy in the video was saying was most likely just an estimate, not an exact figure. No one knows how many starts there are exactly in the universe, but your guess of 10^22 seems fair.
To find how much grain of sand you would need to have 10^22 atoms, simply using molar mass conversions. Use Avogadro's Number to go from 10^22 atoms to # of moles. Then use the molar mass of SiO2 to go from # moles to grams. My calculations (with the units in bold canceling each other out):
10^22 atoms * (mol / 6.02 x 10^23 atoms) = 0.0166112957 mol
0.0166112957 mol * (60.1 g / mol) = 0.9983388704 g
So going by your estimate of 10^22 stars in the universe, you would need about 1 gram of sand to have an equal number of atoms (assuming the sand is completely made up of SiO2).