Word Study - πελεκίζω
Whatever it is, it's fatal and it's done with an axe. In English, "behead" is a pretty nice idiom for that - and it's apparently there in the Greek word - but that doesn't mean the same idiom was necessarily available in Syriac for the 5th-Century translators.
And if there are historic reasons to think the Beast would fatally-axe people in an altogether different way, then yes "behead" might well have stretched the language too far.
In Greek, beheading is what's done with the axe more than what happens to the head. And an axe is somewhat-literally a "choppy-thing". So English may be adding an idea (of the head) but the Syriac is probably losing one (of the choppy).
Which calls for a word-study, and there aren't many extant examples so it's quite a quick one.
https://biblehub.com/greek/3990.htm has the Greek word plesso being used by various Hellenistic writers. I checked Liddell & Scott for the OP - and was able to track down these examples:-
https://archive.org/details/historieswitheng01poly/page/18/mode/2up
Polybius I.7.12
https://www.perseus.tufts.edu/hopper/text?doc=Perseus:abo:tlg,0543,001:1:7:12&lang=original
These were sent to Rome, and there the Consuls brought them into the forum, where they were scourged and beheaded according to custom
Polybius II.30.2
https://www.perseus.tufts.edu/hopper/text?doc=Perseus:abo:tlg,0543,001:11:30:2&lang=original
while the ringleaders were being scourged and beheaded, they neither changed countenance nor uttered a sound
Strabo 16.2.18
https://www.perseus.tufts.edu/hopper/text?doc=Perseus:abo:tlg,0099,001:16:2:18&lang=original
Pompey delivered this place from the tyranny of Cinyrus, by striking off his head.
Ideally we'd have liked a neat reference to Medusa or someone we've got some definite pot-art of them being decapitated. But hopefully this was enough for the lexicographers, with the help of historians, to link the word to axe-decapitation, more than other available forms of lethal hacky-hack.
If there are any history-of-torture types passing, it might be good to know if ancient axe-beheadings were as quick as medieval ones, or if they would have needed repeated blows like πλήσσω < πλάσσω 'to hammer out'
The Syriac Peshitta has https://www.dukhrana.com/peshitta/analyze_verse.php?lang=en&verse=Revelation+20:4&source=ubs
ܘܢܦܫܬܐ - soul, breath of life, self
ܕܐܬܦܣܩ - cut off, cut down, break
I don't know any Syriac. It might be they didn't have a particular word for axe-decapitation and used neutral idiom to keep the key ideas of the "life" being "chopped short". Or it might be this was their particular idiom for it. It might be periphrastic and family-friendly!
But this almost certainly won't be a discrepancy - it's a typical case of three languages with different ways of saying the same thing.
Because it's a translation we can't infer from Syriac saying soul that they didn't mean head - that's drawing a secondary inference from the new language.