Are employers in Abu Dhabi required by law to provide transport?

No , that is left up to them if it is stated in contract , like a transport allowance (money) then perhaps otherwise no. Transportation is "usually" provided for 2 classes of employees , either low skilled workers living in company accommodation or labour camp and as such they have buses to take them to job sites or may be on weekend to town. And the other class are top management who have either their own company car or driver provided ; this is also true for some diplomats. I think we can assume you are in neither of above categories so make a budget for transport.

Also when many employers provide transportation, it's not mandatory to do so. Mandatory are only to pay the salary to your account on time and to get you health insured.

not compulsory , but as per the agreement between the employer and the employee

Absolutely NOT !