Interspecies competition and pathogen
No, you cannot for certain ascribe it to competition, without further information. The mediation by a pathogen is similar to the effects on prey species that are indirectly caused by shared predators (e.g. Prey B increase -> Predator X increase -> more predation on Prey A). Such effects, which can be tricky to separate from direct competition, are usually called apparent competition (see e.g. the classic paper Holt. 1977. Predation, apparent competition, and the structure of prey communities. Theor Popul Biol 12).

However, to some extent, the terminology used may depend on what you view as "the environmental background". All species have lots of adaptations to certain aspects of their living environment, and these naturally differ between species. Some might be more resistant to a certain pathogen (of to drought or other abiotic factors), but this might trade-off against other traits. I that respect, you might view species B as outcompeting species A in a certain environment (e.g. in the presence of the pathogen). However, since you specifically know about the pathogen (which is the focal point of the question), and that species B will probably function as a host/source population of the pathogen, I think it is more useful and informative to label the effect as apparent competition. To partition the direct and indirect effects you will however need moe information.