To modern readers, this often makes Luke's devil sound like Rome's puppet master. But is/was this the case? Did Luke intend to tell us that the Devil rules Earth through his appointees? And is that true? Does Satan appoint Caesars... Kings... US Presidents?
If so, and if Luke was even partly intending his Gospel to be read at Paul's defense, then Luke seems like a total moron to have slipped in such an insult. He may as well have said, 'By the way, Caesar, we believe our God's greatest enemy is the one who appointed you Emperor!' But if not, or if Luke was fully expecting Rome's Emperor to learn of this passage, or perhaps merely if Luke was not a complete moron, then something else must explain what's going on with his text.
Here's my suggestion:
The Latin Vulgate renders "devil" as diabolo, a transliteration of Greek διαβόλου, which meant something like accuser, slanderer or enemy. Thus, any ancient hearer of Luke 4 was introduced to this 'Satan' as a non-credible figure. As far as Nero was [or would have been] concerned, the devil may or may not have presented a vision to Jesus, and even spoken this claim, but the strength of this claim should have been - to Rome's authorities - strictly laughable, especially given the deceiving nature of "devil". To the point, I suggest Luke should have expected this reaction precisely, from Caesar.
These days, if you read Luke 4 theologically then it's fair game to extract this choice nugget and apply it however you
The point of Luke's passage - for Nero's sake - is that Jesus refused Satan's offer. Thus begins a strong anti-political theme running all the way through both Luke's Gospel and Acts. For all Jesus' talk about "God's Kingdom", he obviously meant something else... but as for what, that's a whole other post.
To the point, once again: If we realize that Nero wouldn't have taken the devil's world-rulership claim as sincere, or as valid... then should we? This will seem ironic to some, but as I see it, the greater our faith in the text, the more we might be better off thinking like Nero.
Accepting the temptation as historical fact assumes the quote to have been somewhat accurately reported. Granting Jesus actually did hear the devil's offer that day, and granting that Luke wrote it down somewhat accurately, what we have is a story being told for what it says about Jesus... not for what it says about Satan.
The deceiver could have offered to make Jesus a ham sandwich on Herod's front porch. It would matter no less, and no more. Jesus didn't give in so we'll never know whether the devil was telling the truth.
I might guess that he wasn't... or I might guess that he was... but then maybe the point of the story is that I'm better off not worrying much about world kingdoms, in any event.