Nice question posed. In my opinion, this question strikes at the heart of Shelley's work and the answers received will be very different as this reflects much in way of differences about Shelley's work and thoughts about it. To be "a being" in my mind is offered as character that strive for something. This notion of consciousness that permits individuals to seek an element which is out of their reach could be a critical element in defining what it means to be "a being." For example, I think the monster becomes more than a "scientific creation" when he is expelled and lives out in the wilderness and sees the enjoyment of village life and companionship. When he asks Victor to create a companion, it is the moment where he becomes a being for he understands that there is something which lies outside his condition and yet he strives for it. Victor's desire to create the monster, to appropriate the world in accordance to his own subjectivity, is what helps to define him as a tragic being, but a being nonetheless. This can also be seen in his vengeful pursuit of the monster that lies outside his reach, but remains present in his thought.
In Mary Shelley's "Frankenstein," the young student of natural philosophy and science, Victor Frankenstein, becomes obsessed with acquiring as much knowledge as he can. In so doing, he discovers that with his acquirement of knowledge, he has a power, the power to bestow animation; consequently, he begins "the creation of a human being." However, after having given life to a creature on a "dreary night of November," horror and disgust fills Frankenstein's heart when he beholds what he has given life:
Unable to endure the aspect of the being I had created, I rushed out of the room, and continued a long time traversing my bedchamber, unable to compose my mind to sleep.
Victor Frankenstein calls his creature a "being" because, although it has life, it is not a human being. The word being is a noun formed from the verb to be, which means to exist. Thus being means something having life, something that exists.