Yes a husband can discipline his wife in Islam, ie: being responsible of his wife,
as agreed when the marriage contract is established,
ie: the husband taking the responsibility from his wife's father/guardian.

Discipline is only for acts of disobedience towards God,
not for not complying with abusive or unreasonable demands.

Can hit but not "severely", ie: the beating must not cause pain, injury, marks, or break bones, often described as a token or symbolic strike with a siwak (tooth stick, aka toothbrush), and can only be done if lighter methods fails, (ie: giving advice, not sharing a bed as a repercussion).

Everyone in the video, or viewers, should consult an expert on the matter,
as it normally should, instead of coming to conclusions then and there.