Is linear secret sharing over the addittive group of integers modulo $p$ with $p$ non-prime secure? In Maurer, Ueli. &quot;Secure multi-party computation made simple.&quot; Discrete Applied Mathematics 154.2 (2006): 370-381. I have found the following technique for $k$-out-of-$k$ linear secret sharing:

And the note regarding the domain says this:

Is using as domain $\mathbb{Z}_p$ (additive group of integers modulo $p$) with $p$ non-prime secure? Does it make any difference if $p$ is prime or not? What is the most general definition for the domain (I do not get exactly the meaning of the note)? My guess is that $p$ can be any integer.
What is the most general definition for the domain (I do not get exactly the meaning of the note)? My guess is that $p$ can be any integer.

In short, a domain is the input space. As said the input space can be any domain. Note that the secret $s$ is from the domain, too.
The note simply says that whatever the domain $\mathscr{D}$ is we can simply impose an addition operation on it. Order them, and number them starting from 0. Now, if the number of elements in the domain is $n = |\mathscr{D}|$ then it is equal to $\mathbb{Z}_n$ which is a cyclic group under addition.

Is using as domain $\mathbb{Z}_p$ (additive group of integers modulo $p$) with $p$ non-prime secure?

Yes.

Does it make any difference if $p$ is prime or not?

It doesn't make any difference. This secret-sharing doesn't need the multiplicative inverses. Any finite group can be safe. All we need is the group operations.

As Kodlu mentioned in the comments

This secret scheme can also be defined on the multiplicative groups where the inverse exists naturally. Take each $s_i$ for $1\leq i\leq k-1$ random from the domain and calculate $$s_k = s \cdot s_1^{-1} \cdot s_2^{-1} \cdots s_{k-1}^{-1}$$