This is how Edith Grossman translates it in her version of the Novelas ejemplares (Yale UP, 2016):
https://books.google.co.uk/books?id=lFdlDQAAQBAJ&pg=PA4#v=on...

And other translators render it similarly. Michael Harney (another American translator) renders it as follows in his version (2016):

"with no harm done to any player" (near foot of page, following on from the reference to the "mesa de trucos", which means a billiard table)
https://books.google.co.uk/books?id=IdugCwAAQBAJ&pg=PA10

Lesley Lipson, in Oxford World's Classics (1998), put "without injuring anyone else" (p. 4)
https://www.amazon.co.uk/Exemplary-Stories-Oxford-Worlds-Cla...

I used to have a copy of Cyril Jones's version in Penguin Classics, but I can't find it.

In short, that's what it means.

The DLE definition, "Sin daño o peligro propio o ajeno" ( https://dle.rae.es/?id=BrhkDYt ) , which Cecilia has quoted, is a summary of the early Real Academia definition. The first RAE dictionary, known as the Diccionario de autoridades (1726), defines it like this:

"Phrase con que se explica lo mismo que sin peligro, riesgo, ni gasto u desperdicio de alguno"

From which Henry Neumann also derived his translation, "without injury or danger", in his Spanish-English dictionary (Boston, 1831)
https://books.google.co.uk/books?id=5iJKAAAAYAAJ&pg=PA101&lp...

In other words, without harming oneself or anyone else. But this is already over a century after Cervantes was writing, and a more relevant definition is that of Sebastián de Covarrubias in his Tesoro de la lengua castellana, o española (1611), which is limited to "anyone else", and also offers an explanation of the origin of the phrase:

"Sin daño de barras, suele por alusion sinificar tanto como sin perjuyzio de tercero. Està tomada esta manera de hablar de los jugadores de argolla, quando tirando algún cabe tuercen el argolla, no siendo su intento tirar a ella, sino a la bola del contrario."

"Barras", in the game of argolla (a bit like croquet), means the front of the hoop, which was marked with bars (DRAE 1726). So if you want a literal translation, according to Covarrubias's account of the origin of the phrase, it might be "without bending the hoop". But I don't recommend you put that!

By the way, there's an interesting essay in Catalan here, which provides a useful series of examples of uses of the phrase in the Golden Age. The author defends the theory that it is a mistranslation of the Catalan expression sense desbarrar, as part of a theory that the nasty Castilians stole a lot of their literature from Catalan (another tiresome paranoid Catalan nationalist). I find his argument extremely unconvincing, but it's an interesting read in its way, and, as I say, a useful source of information.
https://www.inh.cat/articles/En-una-sola-frase-i-sin-daño-de...

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Note added at 4 hrs (2019-05-03 22:47:07 GMT)
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By the way, Minsheu, in his A Dictionarie in Spanish and English (1599) defines "juego de barras" as "a play with two bowles and a little round hoope of iron or sylver, with two battle-dores to beate in the boules through the ring": in other words, the game of argolla (as I understand it). I love old dictionaries!
http://www.ems.kcl.ac.uk/content/proj/anglo/dict/pro-anglo-d...