Well the short answer is that he's referring to the them because they were absolutist monarchies at that time, and it's never that strange to see Denmark and Sweden mentioned together, in particular being the two powers of the Nordic area in that era.

It does amount to a sweeping generalization though, and if there's anything that we like in this subreddit, it's to dismantle sweeping generalizations and dig into the details. If you do so (and I doubt Paine did do any close research for what after all is just a passing mention), there's actually quite a lot of difference between how the Danish and Swedish governments were organized at that point in time.

Denmark

In 1658, Denmark had suffered great losses in its wars against Sweden, losing the provinces of Scania, Blekinge and Halland to Sweden (and they remain Swedish to this day) as well as Trøndelag (Trondheim county) in Norway.. Particularly the loss of Scania hurt as it was a quite wealthy province, and had the Danish archdiocese in the town Lund. King Frederik III had managed to repel the Swedish siege of Copenhagen in 1659 and managed to strike back at Sweden in the war of 1660, and regain Trøndelag. As a result he was quite popular in a situation where there was otherwise great dissatisfaction with the government, and Frederik took the opportunity to use that power at the meeting of the Danish parliament or Rigsdag of the Estates, the estates being (in Denmark) representatives of the clergy, nobility, burghers and peasantry, to get the other estates on his side against the nobility. First he was freed from his håndfæstning , coronation vows to uphold the existing laws. Then he instituted absolute rule and hereditary monarchy through the Sovereignty Act of 1661 which was replaced by the Kongelov (King's Law or Lex Regia) of 1665, completing the takeover. Making for a rare case of absolute rule being formally established in written law. After 1660, Denmark would not have another parliament until 1848. But Denmark was not isolated from Enlightenment ideas, and these gained a champion in the mid-1700s in the form of the king's German doctor Johann Friedrich Struensee, who managed to amass a great deal of political power in the power vacuum and struggle caused by the fact that the hereditary king Christian VII had severe mental illness, possibly schizophrenia. The king's brother had stepped in as regent, but Struensee had become close to the queen, with whom he had a love affair, and for a period he was the de-facto ruler of Denmark. In that period he quickly sought to enact a whole set of Enlightenment reforms such as abolishing torture, removing censorship of the press, reducing noble privileges, and liberating tenant farmers from requirements of providing a certain number of days of free labour to their landlords (corvée). To cut short a long and interesting story, Struensee ultimately overreached and ended up being executed by his political enemies in 1772. So many of his reforms were subsequently abolished after his death and old privileges reinstated. On the whole, Denmark did become somewhat more liberal in the period though.

Sweden

On the other hand, in Sweden the country had been pretty democratic for its time in the mid 1700s; the Riksdag of the Estates (same estates as Denmark) held most power rather than the kings. The Sámi minority, which would be very marginalized in the 19th and 20th century had parliamentary representation. Even some women were allowed to vote, although the right was seldom used. However, there was a lot of internal political strife and corruption. The two political parties, the Hats and Caps, were more or less openly being bankrolled by foreign powers (primarily France for the Hats and Russia for the Caps) An illustrative example of how blatant it was; a group of Cap party members of parliament gathered at the Russian embassy to hand over a formal letter of protest. They were angry that after doing Russia's bidding in the election campaign of 1771 and so far in parliament that year, Russia had delayed in paying out their promised bribes, and they demanded over three million dalers of copper coins in reimbursement for their services.

People were not happy about this obviously corrupt state of things, and nor was king Gustav III, who capitalized on this dissatisfaction to take power from parliament in a quick and bloodless coup in 1772, and passed the constitution of 1772 which began the period of 'the Gustavian autocracy', which lasted until 1809 when power was retaken by parliament after public outrage over the wartime loss of Finland and Gustav IV (GIII's son) was forced to abdicate, ending that dynasty. (Sweden is considered a democracy since 1809 then)

Compared to Denmark though, Sweden was much less absolute; there was still a constitution and parliament (women's right to vote was taken away in 1772 though). Parliament retained legislative power, but the king had supreme power over the executive, and on declaring war and such. Sweden could still considered a constitutional monarchy in that period, but it is usually considered to be absolutist monarchy, by comparison to the period before the 1772 constitution and after the 1809 one.

Gustav III wanted to be seen as an 'Enlightened monarch', and swiftly enacted a number of popular reforms not unlike Struensee in Denmark; torture was abolished, the power of the nobility curtailed (to Gustav's own benefit), he was against the death penalty and abolished it for all but the most serious crimes, he issued edicts of toleration allowing Catholics and Jews into the country. On the other hand, freedom of speech regarding criticism of the king and constitution was curtailed.

So in a radically different perspective than what men like Paine advocated, absolutism ('Enlightened absolutism') was portrayed here as the way to achieve the Enlightenment ideas. Gustav III and his taking of power was initially quite popular with the populace and still largely was by 1776 when Paine's Common Sense was published. The first setback in popularity can probably be set to 1775, when a state monopoly on vodka production was introduced and angered the peasantry (who increased illegal distilling of their own).

So to summarize; Denmark had long had one of the strongest absolute monarchies in Europe by that point in time, but was suffering from internal power struggles due to the absolute monarch being incompetent. Struensee had initially public support thanks to his reforms, but lost it due to amassing power to himself and appearing to sideline the king. (whose condition was not really known to the public at large) Although George III of England had his own bouts with mental illness, it's not really comparable to Christian VII. So there was no absolute monarch ignoring the petitions of the people here - on the contrary the people who were actually running Denmark at that time were dependent on public support to be able to do so.

Sweden on the other hand is also an absolute monarchy here (although as said, with a constitution) But it's not really one where (so far) the king had run roughshod over the public but rather enjoyed greater public support than the (nominally) freer and more democratic, but far more corrupt regime that'd preceded him. Gustav believed, or wanted to believe, that he was a champion of the Enlightenment, and certainly portrayed himself that way.

So it was not out of character for Gustav to become the first ruler to recognize American independence in 1777. Even though Gustav's idea of Enlightened rule was radically different than that of the American "Founding Fathers". Paine obviously saw Gustav III as a simple autocrat and the antithesis of his ideas, which is a bit simplistic. Not that I think you'd be able to ever convert Paine to Gustav's way of seeing things. It's unlikely Struensee in Denark, although a radical and reformer, would be in Paine's taste either, not least the fact he had bestowed a noble title (count) upon himself in 1771. Which was one of those moves that'd alienated people from him.

So as said at the start they're just examples of countries that were absolute monarchies at the time. It can't really be anything deeper than that given what was actually happening. At the time, Christian VII was not disdainfully rejecting petitions from his people to satisfy his vanity. He was busy engaging in hallucinations, self-mutilation and public masturbation. Not that Paine would've/could've known that.