Reduction and decidability
In this reduction of $A_{TM}=\{\langle M,w \rangle\mid M\text{ accepts }w\}$ to $L$, what matters in the construction of the Turing machine $M_1$ is  that the language accepted by
$M_1$ is $\{01\}$ iff $M$ accepts $w$, and is $\emptyset$
otherwise.

Whether $M$ does not halt on input $w$, or halts rejecting it, does not make any difference. In both cases, the language accepted by $M_1$ is  $\emptyset$, thus satisfyiing the definition for $L$. Hence $M_L$ will accept $\langle
M_1 \rangle$, so that $M_{ATM}$ will reject.