I have not given these as the reasons for my interpretation. I have said that my interpretation is the traditional one, but I don’t argue that it should be accepted because it’s traditional. And I haven’t said that we should rely on the English text, and have in fact many times said we should be looking detail at the Greek.
The Greek term used throughout the story for the entity possessing the madman is pneuma akatharton (“unclean spirit”). The term is sometimes in the singular, sometimes in the plural. However, there are grounds for translating this as “demon” or “demons”: the term daimonion (generally rendered as “demon” in NT writings) in other Synoptic passages appears to refer to exactly the same unclean spirits; and in this episode (5.15-5.18) the verb daimonizomai is used several times. It means “to be possessed by daimonia”. Thus, the man with the unclean spirits is the man possessed by daimonia (demons).
That said, my interpretation does not rest on the used of the word “demon” in either Greek or English. It rests on the narrative sequence. Something (demons, unclean spirits, whatever they are to be called) asks Jesus for permission to leave the man and enter the swine; Jesus nods to their request (literally “turns toward them”); they enter the swine, and the swine immediately stampede into the lake and are drowned. The Greek words for the transfer are: “having exited [the man], the unclean spirits entered into the swine.”
(Some Greek manuscripts add the adverb “immediately” to the statement of Jesus’s assent, indicating either (a) that Jesus agrees with the demons’ request immediately or (b) if “them” refers to the swine rather than the demons, that Jesus effected the transfer to the swine immediately.)
Note what Mark does “not” say. He could easily have written: “And there was a herd of swine nearby, and after the man possessed by demons frantically entreated Jesus not to send the demons out of the country, the swine stampeded into the lake, and were drowned. And many of those standing by said that Jesus had sent the unclean spirits into the swine.” Had Mark written that, he would clearly have distanced himself from any popular opinion that the pigs had been possessed by demons. But he chose to write what he wrote, and what he wrote says that the pigs were in fact possessed by the unclean spirits which had left the man. It is a straightforward past tense Greek sentence, like the other past tense Greek sentences in the account.
The overwhelming impression of the narrative is that the man was inhabited by a being/beings that were personal agents of some kind, and that these agents were transferred into the pigs. This impression is so strong that the onus is on the person who has the alternate interpretation to show how that interpretation cashes out in the actual Greek words that Mark uses.
I have not asked Jonathan Burke to do anything beyond what Greek scholars routinely do, i.e., interpret passages in accord with the vocabulary, grammar, syntax, idiom, and literary structure. He claims great expertise in scholarship, yet he does not seem to be aware that the core of scholarship (as opposed to an ancillary duty of scholars) is not reading thousands of articles in the secondary literature, but the mastering of one’s primary text. I await his detailed account of the primary text. Until his alternate interpretation is provided, I don’t see how the discussion can get any further.