It is a reference to the Glorious Revolution not the English Civil War.

It was long after Marx, but there was at one time a debate over the role of the Gentry in the English Civil War, the Gentry being small holders and people who rented farms from the aristocracy. Suggested first by RH Tawney, roughly the theory was that, since so much land was being rented by earlier lease agreements that set rents for very long times, by early 17th c. the Gentry were gaining in wealth and the Aristocracy losing, since they couldn't raise rents fast enough. The rising gentry wanted more power to go with their money, were prevented from getting it by the Aristocracy, strife and mayhem ensued. It was put forward by Lawrence Stone and Stone was fiercely attacked by HR Trevor-Roper (...though, I suppose saying "fiercely" is redundant when talking about most things disputed by Trevor-Roper), who maintained that the gentry were actually losing, as they were not in the power center of the King's court. Anyway, it occupied some historians during the 19405's-50's, made researchers start to try to work with big data sources like records of church tithes...I don't know much about the final verdict; J.H. Hexter did a good article on how the statistics didn't seem to bear the weight of such huge claims, and it seems to now be a dead issue. But if it had been significant, it would have been possible to make the Gentry out to be a proto-bourgeois class.

Marx's historical views were influenced by his political ones, and also the understanding of the society he lived in at that time. It would be foolish to take history from Marx at face value, as Marx himself was not really a historian and he was writing a political manifesto.

I believe he and other Marxist and marxist historians are refering to the Civil War period from 1640-1660 which is sometimes called the English Revolution or the Puritan Revolution.

The idea of Class Warfare in the Civil War has pretty much been entirely debunked. The War of the Three Kingdoms is now regarded; thanks to historians such as John Morrill, as not the first war of Revolution but the last European War of Religion. In the 1970's local history started gaining ground in academia and historians started to view the war from a different perspective, far less top down more bottom up. I.e, what collection of local issues can become national issues.

The problem was that within the Long Parliament in 1640/41 religious issues almost always took precedence and was often more radical than the contemporary constitutional reform. In petitions to the Long Parliament such as the Root and Branch the case was also the same, religious petitions garnered far more support from the population, and also far more "air time" in the Commons. Religious issues seemed far closer to peoples minds in the early days of the Civil War than any other factor, in fact in the Second period of the conflict they came back with a resurgence. There is simply not enough evidence to support the assertion that it as a Class War between the emerging bourgeoisie in the town vs the old gentry of the countryside.

Any assertions of a Class War can also be far more easily explained through looking at religion, towns were cosmopolitan the proto-middle class had a strong showing from European Protestant exiles such as the Huguenots, or even just Protestant Europeans such as the Dutch. England was a melting pot of European Protestantism it had been a safe haven during events such as the French Wars of Religion or the Thirty Years War.

These forms of Protestantism were more Calvinist than the offical Church of England doctrine at that time (which was still sort of Calvinist). The official Church Doctrine was percieved as heading in a "papist" direction. Jean Chevalier a Royalist described the changes to the Church in Jersey (which had before the intervention of the English been in a largely Huguenot-Calvinist vein) as "papistical innovations from the days of ignorance." That gives a little bit of an idea for the regard the direction of the State Church hadbeen taken in under Charles I (and Archbishop William Laud). Under Laud altars, fonts, ect. made a return to the church. There was an emphasis on ritual, decoration ect. "the beauty of holiness" All things that a Calvinist would detest, and see as a corruption of the faith, and at this time messing with the church was messing with people's life after death. Charles also wanted to create a more united church which meant new prayer books, the new book was particularly detested in Scotland leading to the Bishops Wars, where the conflict all kicked off if you will.

Even if we say it was a war between the countryside and the town that is overly simplistic, we have more records from towns which can skew our writing. Contemporary Royalst writers tell us there were simply more "Puritans"(a little bit of a misnomer in this case) which is how they lost (Clarendon's history), this gives impression that the direction which the church had been taken in could find few supporters even amongst the countyfolk. Yes Protestantism within towns could also be more radical, but this does not mean that Protestantism in smaller towns, villages ect. was universally in support of whatever the Monarch wanted to do. A lot of people in the countryside actively avoided taking sides in the war at all and conformed to whichever side was in charge at any given time. (I think this was an idea in John Morrills Revolt in the Provinces, but I have seen it repeated in a few places now).

The countryside vs town = old vs new arguemnt also makes no sense as to sustain itself the Royalist cause had to hold towns, which they did. With Charles' ultimate rejection of Laud (too little too late for many) the Royalists did secure a lot of towns, and held them for many years. If it had been the case of town vs country the Royalist cause could not have sustained itself for so long. With Laud out the way you might say the Established Church was regaining a lot of its old lost ground.

TLDR when it comes to the War of the Three Kingdoms in England and Scotland (Bishops Wars), the route cause of the conflict was between two different strains of Protestantism, the result was Monarch on one side, and Parliament on the other. This change in thought is fairly recent, and comes after a lot of research on class war aspects in previous decades, which failed to really answer some big questions.

Whn you start introducing the other Kingdoms it gets a bit complicated, for example the War of the Three Kingdoms sort of started in Scotland, and Parliament largely supported the Scots. However as the Parliamentary faction grew more radical during the war as moderates were thrown out, the Scots and the moderates ended up siding with the Royalists. Its a similar situation in Ireland where the Confederates wanted Catholics to be free to worship, however the Royalists and Catholics ended up on the same side in the end and both were defeated by Cromwell. Most Civil Wars are messy and the War of the Three Kingdoms is probably one of the messiest of them all so I won't go into great detail!

I seem to have gone a bit overboard here, and its a bit muddled. But I hope this answers your question.

but it you want to learn more see if you can grab a copy of Ian Gentles book

or J. Morrill The Nature of the English Revolution (as you can guess from the title he discusses in great depth the reasons behind the Civil War)

The historian Christopher Hill argued that "the English revolution" marked a historic break where power shifted from an effectively absolutist Monarchy to a Parliament dominated by the bourgeoisie.

I don't think anyone tries to argue there are hard or exact parallels between the two events though. I've not got my books with me so I went and dug up an online interview with Hill where he says "One of the things that should be made more of is that no one in England in the 1640s knew they were taking part in a revolution. American and French revolutionaries could look back to England, the Russian revolutionaries had an ideology of revolution based on English and French experience, but no one in England could draw on such experiences. The very word revolution emerges in its modern sense in the 1640s. So that the English revolutionaries are fumbling all the time, they haven’t got a Rousseau or a Marx to guide them. The examples of the Netherlands and the French Huguenots were discussed in the 17th century as religious or nationalist revolts. The only text they could look to was the Bible, but of course the bible says such different things that you can get any theory out of it so that it proved totally unsatisfactory. One of my arguments in my new book is that it was the experience of its uselessness as an agreed guide to action in the 1640s and 1650s that led to its dethroning from its position of absolute authority. That was a major problem for the English revolutionaries, they had no theory to start from." [1]

So it's a revolution because it creates a fundamental rift with the past and it's bourgeois in the sense that it signals the beginning of the end of the power of the aristocracy and the breaking through of the power of bourgeois - what it is not, is the same as the French revolution.

While things have moved on from Hill, I think, the fundamental fact of that power shift is pretty undeniable I think even though there is a whole load more going on than simply a struggle between Parliament and the King.

I think, as someone else mentioned, in the Communist Manifesto the analogy is not intended to be some sort of hard theoretical statement informing all our historical understanding - it's a flourish in a manifesto.

[1] https://www.marxists.org/history/etol/newspape/isj2/1992/isj2-056/hill.html - there are probably better quotes but it was the first thing I found that would do.