To give you a proper answer, we need to define a few more terms than simply "literature". Such as what is meant by "texts".
Defining "text", we need to understand whether or not inscriptions -- anything written or painted on walls, stones, or other objects -- are included. This extends the range from an illiterate person's scribbling what he thinks are letters (and there are examples of exactly this) to the Emperor Augustus' Res Gestae Divi Augusti, one of the longest inscriptions to have survived down to modern times -- and arguably a work of literature. One authority estimates there are about 400,000 inscriptions known, so whether these are included is not a trivial question.
For sake of argument, let's exclude inscriptions. Next, since the Wikipedia definition is a bit vague on this, what kinds of non-fiction writing would we exclude from the category "literature"? Is the Elder Pliny's Natural History literature? He was not trying to write in eloquent language -- as his adopted son Pliny did with his letters -- but to inform people. Yet his Natural History helped establish a genre of literature, the encyclopedia. And then there are a number of howto guides or handbooks that have come down to us of questionable practical value, such as Cato's De Agri Cultura. (Recent studies suggest it was not intended as a guide to farmers, but rather was an essay about a partly imaginary or idealized farm life.) The ancients didn't clearly divide their published writing into "literature" and "practical guides for the general audience" as we do today.
So, again for the sake of argument, let's exclude all texts that were private -- by this, meant to be read by one individual (such as personal letters, financial records, legal records, etc.) -- from the category of literature. What we have left is, by any measure, overwhelmingly literary. What private texts that survive are few: a few hundred pieces from Britain (most of which comprise a few, disjointed words), maybe a hundred more from Pompeii and Herculeneum, and a similar number from Vindonissa (a Roman military camp in what is now Austria), Dacia (a series of miners' contracts), and North Africa (a number of letters on ostraca). These private texts (without critical apparatus and commentary) would fill maybe a couple of printed volumes at most, as compared to the 50+ Latin titles of the Loeb Classical Library which comprise close to 100 volumes. This should not be surprising: transmission of texts before printing was done through copying by hand, and few people will bother to copy theirs or other peoples' private papers.
In other words, where maybe 4% of the cuneiform texts are literary, with Latin it is the opposite situation: maybe 4% are non-literary, not counting inscriptions.
And to anticipate your next question, the situation with ancient Greek texts is complicated, due to the survival of so much writing on papyrus from Egypt: on the one hand, there are hundreds of volumes of published papyrus texts (which is still only a fraction of the surviving texts); on the other, there are hundreds of volumes of "literary" Greek writings that have survived to today. And there remains the question how do we categorize all of the inscriptions in Greek, which are at least as abundant as those in Latin...
