have no business

“Branislav Ivanovic with a volley of technical precision, absolutely nails it … - but a yard too high. Probably less.
Right-backs have no business hitting the ball that well…”

–Do you hear any irony\admiration there or the author seriously considers it being not their business shooting on goal instead of playing defensively?

It’s not a ‘serious consideration’. He’s saying that Ivanovic has an ability he wouldn’t expect to see very often in a player in that position.

Yes, there is a touch of irony there. ‘Have no business’ here suggests ‘shouldn’t’ ‘has no right to’ said in a lighthearted manner. There is a short story by W Somerset Maugham - The facts of life, in which a father gives his son advice on how to behave on his trip to Paris. He tells him among other things never to gamble. The son ignores his father’s advice and gambles and wins a huge amount of money. The father tells his friends - He has no business winning all that money. His friends all see the funny side but the father is really annoyed.

Thank you.
As an aside, the book called Somerset and All the Maughams, along with his works, served for me some decades ago, as a guide into English.