Marcus Aurelius almost certainly did not believe in these things in any meaningful sense; if he did, he was not the first; and regardless of whether or not he believed in them, he did not try to make them a reality.

The passage occurs in the opening of his Meditations (1.14.1), where he lists a number of other people who influenced his thinking. It'll be useful to see this passage in the original Greek, for reasons I'll explain below:

Παρὰ τοῦ ἀδελφοῦ μου Σεουήρου (...) φαντασίαν λαβεῖν πολιτείας ἰσονόμου, κατ̓ ἰσότητα καὶ ἰσηγορίαν διοικουμένης, καὶ βασιλείας τιμώσης πάντων μάλιστα τὴν ἐλευθερίαν τῶν ἀρχομένων:

From my brother Severus (...) I received the idea of a polity in which there is the same law for all, a polity administered with regard to equal rights and equal freedom of speech, and the idea of a kingly government which respects most of all the freedom of the governed...

The first thing to note is that this single sentence is the whole of his thoughts on the matter. He doesn't have more to say on it here or elsewhere. He is simply listing ideas and traits he learned from other people; Severus is credited with a long list of other things besides this, like love of family and commitment to philosophy, and none of these is afforded more weight than the others.

The second thing to note is that 'idea' is a pretty generous translation of the Greek word Marcus Aurelius used to describe a constitution based on equality and freedom of speech, which will sound familiar enough to English speakers: phantasia. The word tended to refer (then as now) to images, visions and apparitions - not real and tangible things. At best, our Marcus is saying that he learned from Severus to entertain this notion in the abstract, as a thought experiment. He never even says whether or not he thinks it has potential.

What did this thought experiment mean to him? Here's where the Greek really matters. Marcus Aurelius styled himself a Stoic - a philosopher adhering to a school of thought that had developed on the colonnades (stoas) of the Athenian market square (agora). This was a thoroughly Greek philosophical tradition, and we can take it for granted that Marcus Aurelius would have read and contemplated a great deal of Greek writing on philosophy and history. Generally, the Roman educated elite looked to the Greeks as masters of oratory and philosophy, and a considerable amount of any wealthy Roman's education would consist of reading Greek literary classics and thinking about the differences between Greek and Roman culture and society. This is why the very Roman Emperor Marcus Aurelius wrote his Meditations in the language of all philosophy worthy of the name: Greek, not Latin.

A convenient part of using Greek to describe an idea like the one above is that it already had the vocabulary to describe it. The words used in the passage above were well established in Greek historical and philosophical works: isonomia (equality before the law), isotês (equality), isegoria (literally "equality of the marketplace", but meaning freedom of speech), and eleutheria (freedom). Why did Greek have all these words? Because there had already been a society that defined itself entirely by these values: the democracy of Athens.

As a form of government, democracy first occurs in our sources under the name isonomia - equality before the law. The core principle of the democracy that was installed at Athens in 507 BC and fully established about 461 BC was that every adult male citizen had the same rights as all the others. There was no property requirement for voting or sitting on councils or acting as magistrate (with a few exceptions); no group was privileged in the law courts and the political system was designed in such a way that no single clan or faction could dominate the government of the state. It was this isonomia that set Athens aside from other Greek states, most of which excluded the poor from power. It was not until the end of the fifth century BC that this form of government came to be known by its famous name, demokratia - people power.

Greek authors of the Classical period gave much thought to the Athenian idea as it spread through the Greek world, and big names like Plato and Aristotle had a great deal to say on democracy and its guiding principles. It's not surprising, then, that Marcus Aurelius' musing on a constitution based on legal equality reads like a checklist of Athenian democratic ideology. Democratic Athens was a society built on the concept of equal rights for all, and one that could only function if all citizens had a protected right to speak (in the agora and the Assembly) rather than silently accepting the judgment of their social superiors, as was expected of the low-born in other Greek states. It was a form of government that assumed and defended the freedom of all its citizens rather than oppressing some for the benefit of others (or so they said; they never questioned their systemic oppression women and enslaved people). The specific link between equal rights and freedom of speech is fundamental to Athenian democracy; one could not exist without the other. There is even some evidence that Athenians frowned on and suspected people who never used their freedom to speak in public, since democracy could not survive if the people didn't contribute.

In short, all our Marcus is really saying is that, at Severus' suggestion, he spent some time reading up on Athenian democracy. To him, it was just one of the more quaint and radical experiments in government that had been tried in the distant past - suitable for a thought experiment, but not for real-life application. There are two key concepts notably absent from this paragraph: first, the proper name for this "polity of equal rights", that is, demokratia (democracy); and second, the infamous corollary of freedom of speech, parrhêsia. This word also means "freedom of speech" but more in the sense of bluntness, the assumed freedom to speak with no regard for propriety or respect, which is not what we mean by "freedom of speech" in a legal sense, but tends to be what we mean by it in everyday use. In the eyes of Greek authors, this parrhêsia was what made Athenian democracy particularly hard to stomach: who did these penniless Athenians think they were, shouting abuse at their betters, when in other states they would be little better than slaves? It's understandable that these are the two specific concepts missing from Marcus Aurelius' text. They are the more subversive elements of Athenian democratic ideology, and the parts least compatible with the rule of an emperor. Our Marcus is happy to consider equality, but stresses that it has to be under the stern eye of a king.

Interestingly, the word parrhêsia does occur in the Meditations, just a few paragraphs above the one we're discussing here. Among other wonderful things, such as not to believe in mystics and not to waste time raising quails, Diognetos taught Marcus Aurelius "to endure freedom of speech". Here the word is not isegoria but parrhêsia. The emperor, far from encouraging and establishing it, had to learn to endure it - to be patient when people surrounding him would just say what they thought instead of bearing in mind whose august presence they were in. This shows the more natural attidude of a Roman emperor to the idea of Athenian freedom of speech. Naturally, he could not do more than bear parrhêsia, and would never consider the sheer anarchy of a state in which it was protected by the law.

It is from the missing elements in his line about a constitution of equal rights that we can see his (and the general Roman) attitude to Greek democracy. From all Roman authors throughout the Republican and Imperial periods, we get a sense that Roman elites may have admired Athens for its cultural and scientific achievements, but that they despised and mistrusted its form of government. In their view, the people had far too much power and freedom in these democracies, and the result was a state of semi-anarchy that made them ineffective as states and unreliable as allies. In their dealings with Greek states, the Romans greatly preferred to work with oligarchies and wealthy individuals, rather than unruly and unpredictable assemblies. Freedom and equality were all well and good, but they had to have their limits; the state had to be governed by those best suited to the task. The Greeks had democracy, but the Romans had the Republic, in which the poor had a voice, but the rich called the shots.

For centuries during the Classical and Hellenistic period, despite its endless wars and rapacious tyrants and kings, the Greeks knew democracy in one form or another. But by the time the Romans dominated the Mediterranean, all democratic systems of government were gone. By the first century BC, all Greek states were effectively run by narrow oligarchies of those wealthy men who could boast the closest ties and the greatest good will to Rome. In other words, it was the Romans who finally extinguished the spark of democracy; it was their new supremacy that destroyed any alternatives to the type of government they preferred. The irony of Marcus Aurelius' idle musings on some carefully selected principles of Athenian democracy is that he was the emperor of the people who finally killed it, and whose legacy ensured that no one anywhere in the world would seriously consider democracy as a form of government for two thousand years.