Their definition is very skillfully worded. At this point in time, I do not believe that vegans are enemies of the gospel. One, this is a philosophy, which is a creature of culture/society, and in this case rightfully so. As culture/society changes(for the better), philosophy does as well. Their wording/definition is open to this interpretation as well, in a favorable light. They make it a point to emphasize exploitation and cruelty. Exploitation is associated with profit and selfishness. And, genesis does not advocate for either of those, especially if cruel. The genesis argument is a poor one against veganism.
Do you actually know any philosophical vegans? In my experience, these are people who value animals over humans, showing concern for animal rights while accepting abortion.
A philosophy that actually opposes exploitation and cruelty would focus on the reform of farming practices. Such do exist, for example, the biodynamic agriculture and permaculture movements. Veganism is defining any use of animals for food, cruel or not, as exploitation. This view is in opposition to Genesis.