Playful? Utopia? Yes, really. Just because some of the issues at hand are serious, doesn't mean More isn't having fun with this whole invent-your-own world thing. You know all those funny names that appear in the book? A lot of them are actually puns on different Greek words—including, you know, the title. That's More having a blast. He's not only sneakily naming characters and people things like "speaker of nonsense," but he's also showing off his Greek skills.
Utopia is also playfully systematic. That's right, it employs its playfulness in a pretty systematic way. The text is divided into two sections called Books: the first is a debate about politics and philosophy while the second is the description of Utopia. Within the description of Utopia, there are handy-dandy subdivisions, like "Warfare and Slaves," that organize all that descriptive info.
But the most systematic aspect of the text would be its format as a dialogue. No, we don't just mean people talk a lot (although, they do), we mean that More is using an old and respected philosophical format to organize his book: the (Platonic) dialogue.
Made famous by our old friend Plato, the dialogue was a very popular Renaissance format that (1) had a quick little back-story called the "frame" and (2) mostly described a long conversation between two or more acquaintances about any number of philosophical topics. So, even though we might find the back and forth conversation between these characters a bit tedious, and even hard to follow, for Renaissance readers it would have been a very familiar and systematic way to organize a text.
And just in case you're still perplexed by how a long, philosophical discussion can be playful too, it's helpful to know that not all philosophical dialogues were serious. (Gasp. We know). In fact, one of More's absolute favorite Greek authors, a guy named Lucian, invented comedic dialogues, which are full of complete silliness.
In case all of More's ancient Greek word games weren't enough dead language fun for you, don't forget that More also wrote the text of Utopia in Latin. And guess what? He had some fun with it.
While Latin is incredibly systematic language, almost mathematical, it's also very flexible. Word order? Not a big deal. Subjects, objects, verbs, and all that good stuff can be pretty much in any order you want. And More goes a little nuts with this, constructing all kinds of wacky Latin sentences that sometimes makes reading the text in the original almost like solving a puzzle.
But, you ask, wasn't More English? Why isn't he writing in English? (Why?!) When he wrote Utopia, Latin was the international language of the highly educated—the people More would have expected to be reading his text. English, along with all the those other languages like French, Italian, and German were called the vernaculars, and were considered to be less sophisticated than Latin. Funnily enough, that's all about to change only a few year after More writes Utopia (hello, Shakespeare!) and it gets translated into those unsophisticated vernaculars very quickly. In fact, Utopia was read so much for frequently in translation that people rarely look at the Latin today.