If a have an operator $\circledast:A\times A\rightarrow A$ and $a,b,c\in A$, then the expression $$a\circledast b\circledast c$$ Can be interpreted only as $(a\circledast b)\circledast c$ or is possible to interprete it as $a\circledast (b\circledast c)$?
Regardless if $\circledast$ is a associative or nonassociative operator.
And no matter if it's seen by a left-to-right reader (as a japanese person) or a right-to-left reader (as an english person).
On
Even though your answer has already been answered, it's important to notice that your expression doesn't make sense unless $$ \circledast: A\times A\times A \to A. $$ In this case, associativity doesn't matter and you can write $a\circledast b\circledast c$.
On the other hand, if your operation is defined as $\circledast:A\times A\to A$, something like $a\circledast b \circledast c$ isn't even defined a priori until you define the associativity.
If $\circledast$ is not associative then in general $$a\circledast (b\circledast c) \neq (a\circledast b)\circledast c$$ so just writing $$a\circledast b\circledast c$$ would be ambiguous, unless we follow some convention of right of left associativity. As far as I know, when you see something like $a\circledast b\circledast c$ the operator $\circledast$ is taken to be associative, otherwise brackets would be added. So that means that you can then take $a\circledast (b\circledast c) $ or $(a\circledast b)\circledast c$ because these two are equal by associativity.