The question of Being aims therefore at ascertaining the a priori conditions not only for the possibility of the sciences which examine entities as entities of such and such a type, and, in so doing, already operate with an understanding of Being, but also for the possibility of ontologies themselves which are prior to the ontical sciences and which provide their foundations. Basically, all ontology, no matter how rich and firmly compacted a system of categories it has at its disposal, remains blind and perverted from its ownmost aim, if it has not first adequately clarified the meaning of Being, and conceived this clarification as its fundamental task.
Being and Time, Introduction, 1927
|Ortega (left) and Heidegger (right) in Germany, 1951|
As to the issue of who was first in raising the need to revise the traditional concept of Being in a revolutionary, existentialist manner, see this Stanford Encyclopedia of Philosophy article (beginning with the third paragraph in part 6 of the article). Regardless of who published what first, the reality is that these two contemporaries raised very similar issues at about the same time. Which one did a better job of philosophical analysis is a judgment left to the musings of the philosophical reader. (You know my judgment.) What is key here is that both Heidegger and Ortega very explicitly and self-consciously wrestled with the great Western philosophical tradition in order to explore further and revise the traditional concept of Being. The lesson here is to enter that great philosophical tradition and to take it seriously and to surpass it.