Is what is paid to the Zakat and Income Authority by owners of institutions and companies, at a rate of 2.5% of the capital, considered a legitimate zakat, or am I obligated to pay another zakat in addition to this amount?

As long as it was requested from you in the name of Zakat and you disbursed it with the intention of Zakat, then it is Zakat. This is because the ruler (Wali al-Amr) has the right to request Zakat from the wealthy to spend it in its rightful channels. You are not obligated to pay another Zakat on the wealth for which you have already paid Zakat to the state. However, if you have other wealth or profits for which you have not paid Zakat to the state, then you must disburse it to those who are deserving among the poor and other eligible recipients of Zakat.