I think it’s a very poor way to express what is meant here. The idea is that the difference between the infinitive and the past participle of verbs is marked in French, it’s always the case in writing :

• paré/parer
• fini/finir
• cru/croire

However, in spoken French, for many verbs, those from the so-called first group ending in -er in the infinitive, the past participle and the infinitive sound exactly the same :

• paré = parer transcribed /pare/ in IPA notation

I would have said to express this idea :

• La différence entre l’infinitif et le participe passé est marquée phonétiquement sauf pour les verbes du premier groupe.

Se jouer gives the impression that something is in play, at stake, is not settled yet, which is not the case here. For example, you could have :

• La paix du monde se joue au Conseil de sécurité des Nations Unies.

The only way I’d use jouer in your sentence is without the se as a loose synonym for producing some kind of effect:

• La différence entre l’infinitif et le participe passé joue jusqu’à la phonétique ce qui ne se fait pas au premier groupe.

But the phrasing is not very good.

The relevant definition in the French-English Larousse is found Under “se jouer” and is the second one in that section;

(soutenu) [produire un effet]

It corresponds to TLFi II A 1 emploi pronominal réfléchi;

Emploi pronom. réfl.

• Un ruisseau qui se joue dans la prairie (Ac. 1835-1935).
• Autour de ce bâton, dans des méandres capricieux, se jouent et folâtrent des tiges et des fleurs (BAUDEL., Poèmes prose, 1867, p. 313).

Au fig. Se donner libre cours.

• Je vous encourage fort à nous faire connaître les personnages de cette grotte : laissez votre imagination se jouer à son aise : elle est belle, tendre et féconde (CHATEAUBR., Corresp., t. 1, 1803, p. 125).

There seems to be a problem of ajustment, the possible omission of semantic variants in the dictionary definitions;
the difference between “avoir libre cours” and “se donner libre cours” is a thin one; for instance, in the last example, saying “laissez votre imagination avoir libre cours” and “donnez libre cours à votre imagination” mean the same thing; moreover, if we apply the definition verbatim in that example, we have a less usual variant where the imagination takes on the part of the subject (“laissez votre imagination se donner libre cours”) but the meaning remains very close.

In truth, the term which seems most relevant is “se produire” or similarly “avoir libre cours” and not “produire un effet” or “se donner libre cours”. There is, to compound the diffilculty in this sentence, a term not quite non logical: “ce qui ne se fait pas”; the meaning of “faire” does not correspond to the context: in the negative form “se faire” does not mean “se produire” (TLFi, faire² II A 2) and anyway the form is too different (il se fait que). The deduction that the negative form is not defined is mine and I find no confirmation for it in the linguistic literature.

• Il se fait que ces choses-là arrivent.
• Il ne se fait pas que des gens restent sans manger aussi longtemps.

It seems that there does not exist another sens of “se faire” that will fit this context; in particular “se faire” cannot be used as a proxy verb for “se produire”.

The proper verb would have been a verb such as “être le cas” in a form such as “ce qui n’est pas le cas”.

• La différence entre l’infinitif et le participe passé a libre cours jusqu’à la phonétique, ce qui n’est pas le cas au premier groupe. (ce qui ne se passe pas, ce qui ne se produit pas)

• La différence entre l’infinitif et le participe passé se produit jusqu’à la phonétique, ce qui n’est pas le cas au premier groupe.

This means that the difference between the two forms is carried over from the spelling to the pronunciation.

entendre/entendu ==> ɑ̃tɑ̃dʁə/ɑ̃tɑ̃dy (the difference carries over to the pronunciation, is still present in the pronunciation)

chanter/chanté ==> ʃɑ̃te/ʃɑ̃te (does not carry over to the pronunciation)

I think the sentence is simply incorrect.

La différence entre l’infinitif et le participe passé se joue jusqu’à la phonétique ce qui ne se fait pas au premier groupe.

“ce” makes reference to “la différence phonétique”. But it’s not good syntax to my knowledge. They mean :

• La différence entre l’infinitif et le participe passé se joue jusqu’à la phonétique. Il n’y a pas de différence pour le premier groupe.
• Difference between past participle and the infinitive comes down to phonetics. There is no difference for the first group.

As it is already well explained in other answers, the past participle and the infinitive form of first group verbs sounds the same (the others dont). Which is very confusing for a surprising number of french people as well.

Concerning “se jouer”. As in other languages, a game is played (“game” is used in a passive way):

• Je joue à ce jeu. Ce jeu se joue en intérieur
• I play this game. This game is played indoors.

By extension it can be used when two things are in opposition.
“Se jouer à” is a rather common french expression. It refers to the things that made a difference.

For instance, a boxing match where a commentator would say:

• Ca va être dur pour les juges de choisir un vainqueur, ça se joue à un coup de poing ou deux !
• It will be hard for the juges to decide on a winner, it’s down to a punch or two !

The most usual form I can think of is “ça se joue à peu” which could be translated in some contexts to “it’s a close one”. It can be used for anything. For instance:

• Tu préfère ce bleu ou celui là ?
• Hmmm, dur à dire. Celui là, mais ça se joue à peu…

Which translates to:

• Which is your favorite blue ?
• Hmmm, hard to say. This one, but it’s a close one…

So, by saying:

La différence entre l’infinitif et le participe passé se joue jusqu’à la phonétique.

It means that you cannot make the difference until phonetics.