Is working for an institution or company affiliated with a state that does not rule by what Allah has revealed considered one of the nullifiers of Islam, rendering its doer an apostate?

There is no sound basis for such a statement, nor do we know of any imams of knowledge who held this view. The ruling on working in government jobs in states that do not rule by what Allah has revealed varies depending on the type of job. If the job involves legislating or enacting laws that contradict the Sharia, then it is disbelief (kufr). If it involves aiding oppression or defrauding people of their rights, then it is wickedness (fisq) and disobedience (ma'siyah). However, if it is free from legal prohibitions, then it is permissible.