Until we find an infectious cause of obesity, calling it an obesity pandemic is a rhetorical act it grounded in the widely accepted meaning of the word.
A pandemic is a form of epidemic (according to Wikipedia's definition, which you have referred to).
An epidemic is an outbreak of a disease (according to Wikipedia's definition, which you have referred to).
A disease is a particular abnormal condition that negatively affects the structure or function of all or part of an organism, and that is not due to any immediate external injury... A disease may be caused by external factors such as pathogens or by internal dysfunctions. (according to Wikipedia's definition, which is included by link by its definition of epidemic).
There is no requirement on the definition of epidemic that you have referred to that requires it to be infectious.
Please pick a definition and stick to it. You want a pandemic to be a global outbreak of a disease to which the overwhelming majority of the population is susceptible and which is spread via a pathogen without physical contact. If there's an authority that uses that definition, find them and cite them. Otherwise please stick the definitions you've already cited and move on.
The wikipedia definition of epidemic that I cited uses the phrase "rapid spread of disease". I think most people would agree that for a disease to spread it must be communicable in some way.
Wikipedia's page on Adenoviridae lists these human adenovirus types that cause obesity or adipogenesis: HAdV-A type 31; HAdV-C type 5; HAdV-D types 9, 36, 37
One of the references:
Voss JD, Atkinson RL, Dhurandhar NV (November 2015). "Role of adenoviruses in obesity". Reviews in Medical Virology. 25 (6): https://zenodo.org/record/1229348
So yes, obesity can be caused by contagious disease.
Obesity can be caused by a infectious disease is not the same thing as obesity, in general, being caused by an infectious disease. It would have to be caused by a contagious, in general, to be able to describe the widespread prevalence of obesity as a pandemic, since the term pandemic is concerned with infectious diseases.
