Ne arbiter quidem hunc iactum intellegit.

It means not even.

So ne arbiter quidem means not even the judge/umpire/referee. This is a very common Latin way to add emphasis.

Because that is how the idiom works in Latin.

In ne ... quidem, the word or phrase placed between ne and quidem is the part being emphasized. Here the emphasized word is arbiter.

So:

• ne arbiter quidem = not even the arbiter

Latin often does this with fixed expressions that English keeps together.

Because arbiter is the subject of intellegit.

The verb intellegit means understands, so the person doing the understanding must be in the nominative:

• arbiter = the arbiter / judge / umpire
• nominative singular

So the basic structure is:

• arbiter intellegit = the arbiter understands

Then ne ... quidem adds the idea not even.

Hunc iactum is accusative singular, and it is the direct object of intellegit.

That means it answers the question understands what?

• hunc = this (masculine accusative singular)
• iactum = throw / cast / move (accusative singular)

So:

• hunc iactum intellegit = he understands this throw/move

With the negative expression added:

• Ne arbiter quidem hunc iactum intellegit = Not even the arbiter understands this throw/move

Because hunc has to agree with iactum.

Latin adjectives and demonstratives must match the noun they go with in:

• gender
• number
• case

Here iactum is:

• masculine
• singular
• accusative

So the correct form of hic is:

• hunc

That is why Latin says hunc iactum = this throw/move.

Iactus is a fourth-declension noun.

Its dictionary form is usually:

• iactus, iactus = throwing, throw, cast

Even though many fourth-declension nouns end in -us in the nominative singular, their accusative singular often ends in -um.

So:

• nominative singular: iactus
• accusative singular: iactum

That is why the sentence has hunc iactum.

Intellegit is:

• third person singular
• present tense
• active voice
• indicative mood

It comes from intellegere, meaning to understand.

So intellegit means:

• he understands
• she understands
• it understands

Here the subject is arbiter, so the meaning is the arbiter understands or, with the negation, not even the arbiter understands.

Yes. Latin word order is much freer than English word order.

A few things are especially important here:

• ne ... quidem normally surrounds the emphasized word
• the verb often comes near the end of the sentence
• the object can come before the verb

So this order is perfectly natural:

• Ne arbiter quidem hunc iactum intellegit

A more mechanical rearrangement into English-style order might look like:

• Arbiter ne quidem hunc iactum intellegit

But classical Latin prefers the idiomatic placement ne arbiter quidem.

Because ne ... quidem is the normal idiom for not even.

So:

• ne ... quidem = not even

This is different from plain non, which is the ordinary word for not.

Also, quidem by itself often means something like indeed or at least, so the full negative meaning comes from the fixed combination ne ... quidem.

It is the same word in spelling, but here it is part of a fixed idiomatic expression.

So in this sentence, you should not think of it as:

• a negative command
• a purpose-clause marker

Instead, you should recognize the whole expression:

• ne ... quidem = not even

That is the important thing for understanding this sentence.