what is "the argument" of Jesus in Luke 24:39?

Fourfold answer whose summary is that "ghost" (or "spirit") seems to be a legitimate translation.

1. Ancient Greek has another word for "demon".

This word (e.g. in 1 Tim 4:1) is δαίμων daimōn. As Lesley's answer points out, Jesus uses a more general word (πνεῦμα pneuma) connected to the idea of "spirit".

2. Hebrews 9:27 doesn't clearly rule out ghosts.

It's not clear to me that Hebrews 9:27 inevitably rules out the existence of ghosts, or at a minimum the translation "ghost", insofar as that word refers to a spirit or a manifestation of a dead person.

• Ghosts may still only die once and face judgement at some point afterwards.
• Ghosts may not be or may not have been people (but some other supernatural entity).

However, it may still be a possible interpretation. I don't know the hermeneutics of that passage.

3. The Bible features people who appear in non-physical form after they've died.

Saul consulted a medium to speak with Samuel at Endor (1 Samuel 28:3-25). Saul "recognized" that it was really Samuel and Samuel asked why he had been "disturbed" for this meeting. He had died by this point and was apparently in some other state from which to be disturbed.

More contemporaneously, Moses and Elijah appeared alongside Jesus during the Transfiguration (Mark 9:2-13). They appeared out of nowhere and disappeared in a cloud.

One might argue that if what the disciples thought was the ghost of Jesus was the same kind (good) as the manifestations of Moses and Elijah, they wouldn't have been frightened of him. But in fact they were frightened at the Transfiguration too (Mark 9:6), and people generally are frightened of divine apparitions in the Bible.

To my mind, this could easily be a parallel to what the disciples thought they were seeing. Does it matter for our point whether they were actual ghostly spirits present in some way or, for example, just optical visions? Either way the disciples had something to mistake Jesus for.

4. Jesus sometimes answers people according to what they know.

Belief in ghosts was common throughout the ancient Middle East, and Jesus sometimes answered people according to what they knew rather than addressing the incorrect presuppositions in their statement. He sometimes cut to the heart of what they wanted to know.

We can see parallels in many passages in which God speaks in the Old Testament. He chose to adopt the Hebrew idiom and cosmology, because that was what made sense to the people He was talking with. The Bible fits naturally into Middle Eastern mythology (in some ways) not because God is ultimately a Babylonian deity but because that was the flock He was shepherding.

To apply this to Jesus' post-resurrection apperance, what was important in the disciples' claim? That they believed he was still dead, or that he wasn't really there, resurrected in the body. So rather than explain to them why ghosts aren't real despite the things they believed and had seen, he cut to the heart of their doubt and showed them a proof they would accept.

However, Luther thought ghosts were devils

Luther gave at least one sermon in which he expressed a similar opinion to the one cited in your question. Although he would use "ghost" or "spirit" to translate these passages, he believes that they are not the souls of dead human beings but some kind of spiritual being allied to the devil:

Christ does not deny it but confirms with His answer that spirits do appear ... However, Scripture does not say or give any example that these are the souls of dead people ... Scripture says nothing anywhere about the souls of dead men who have not yet risen going about among the people ... they are now divided and separated completely from the world and from this time. ... All those ghosts and apparitions which are seen or heard, especially with rumbling and rattling, are not the souls of men, but surely devils.

I'm obviously not qualified to gainsay Luther, but I hesitate to accept the claim that Scripture says nothing anywhere about the souls of the dead who haven't yet risen (Luther even adds that there is "not one word"). Also worth noting is that in the rest of that sermon, there's the usual Lutheran contrast with papist beliefs. The nature and status of the unresurrected dead is a subject on which Catholicism had a surprisingly specific claims to make, which Luther did not like.

Unfortunately, I don't know what the other Reformers such as Knox, Zwingli, and Calvin thought.