It's essentially derived from the sexual sense of "tease" (familiar to many in the rather coarse term prick-teaser - a woman who tries to make a man sexually excited but does not intend to have sex with him). Also familiar, rather less coarsely, in striptease.
The sports commentator is saying that Barnes is tempting Alexander-Arnold to play "down the left". Perhaps by leaving some open space there on the wing (that Barnes is responsible for "guarding"), because Barnes knows that he can run faster than Alexander-Arnold - so if the latter tries to make a run down that wing, Barnes will easily be able to catch him up and prevent him setting up a chance to score.
EDIT: Or it could be tease in the sense of taunt (insult, jeer at, make fun of, ridicule). If Barnes is a much better player than Alexander-Arnold (something I know nothing about), the intended sense might simply be that Barnes "runs rings around" his less agile opponent. Which of these two meanings applies would be more obvious to readers with more in-depth knowledge of the players.
I don't think there's any implied allusion to tease = gently pull or comb (tangled wool, hair, etc.) into separate strands in OP'd exact example. But in principle I could accept Barnes teased the ball through the defenders as meaning he "dribbled / nursed" the ball in a relatively straight path through / past several opposing players.