The sense of competence is really important.
Also important are the sense of belonging to the Home Team - boys in particular need a team ime, and the feeling of having a trusted role in a team. Sports or musical ensembles can also fulfill this need but chores are free, require no special equipment and nobody gets their eardrums pierced by beginner clarinet practice...
Perhaps overlooked is the amount of parental effort that goes into organising and motivating a child to do chores and keep at them consistently, and the effect of this on the child.
If done right, i.e. without nagging or threats or bribes or worst of all, sarcasm, the closeness to the parent that results from teaching and then gently monitoring can greatly enhance a child's sense of self esteem. The parent can encourage and praise (in a measured way) and show by their own commitment to consistency, patience and positive interaction, and maybe above all their belief that the child can learn and can master what is expected, how to work with others respectfully.
It takes effort and commitment on the part of the parent to keep a child at a daily or weekly chore, and this example rubs off on the child.