The question describes the development of a diploid gametophyte from a diploid sporophyte cell without the involvement of meiosis. This is a key characteristic of apospory.
Let's break down the terms:
Sporophyte (2n): The diploid phase of the plant life cycle.
Gametophyte (n): The haploid phase of the plant life cycle.
Meiosis: A reductional cell division that produces haploid cells from diploid cells.
Mitosis: An equational cell division that produces genetically identical diploid or haploid cells from diploid or haploid cells, respectively.
Apospory: This is the development of a gametophyte directly from sporophyte cells (such as somatic cells of the nucellus or integuments) via mitotic divisions, bypassing meiosis. If a diploid sporophyte cell undergoes mitosis to form a diploid gametophyte, this is apospory.
Diplospory: This is a specific type of apospory where the megaspore mother cell (which is diploid) undergoes a modified division (either complete or incomplete meiosis, or sometimes mitosis) to produce a diploid embryo sac (gametophyte).
Apogamy: This is the development of a sporophyte from a gametophyte without the fusion of gametes. This is the reverse process (n $\rightarrow$ 2n sporophyte).
Parthenogenesis: This is the development of an embryo from an unfertilized egg cell. Typically, in plants, an egg cell is haploid, so parthenogenesis would lead to a haploid sporophyte.
Given the question states a "diploid sporophyte cell" produces a "diploid gametophyte" without meiosis, this aligns perfectly with the broader definition of apospory, where diploid sporophyte cells (somatic or reproductive precursors) give rise to a diploid gametophyte. Diplospory is a subtype, but apospory is the general term fitting the description.
Final Answer: \(\boxed{C}\)