managed to get it out after watching a similar battery clip of a different manufacturer. video you posted shows a different model though
my type of battery is on T300CHI-F1-DB, T300LA-13NB02W1M28011, T300LA-BB31T, T300LA-C4001H, T300LA-C40, that seems to be different
if anyone needed, fist you slightly slide the metal clip outside, enough to clear the white connector, then just pull up (like on retina macbooks) on the white connector from the sides using fingernails.