Why should we use dolgozom here, not dolgozok? Isn't the dfinite conjucation used only when there is a definite object?
This is not the definite conjugation (dolgozik doesn't even have one), but a special property of this group of verbs whose base form ends on -ik. Their 'én' form is mostly(!) -om (or -em or -öm, depending on the vowel harmony), but can also be -ok (-ek, -ök). Which suffix to use can depend on region and personal taste, but for the more common ones (eszik, iszik, dolgozik, lakik, költözik, and so on) it sounds better to use the -m form. But neither form is outright wrong.