Can one construct OTPs without using XOR?
Both constructions are not perfectly secure!



In an attempt to express things a bit more mathematically, I'd say you can implement a one-time-pad with a message $m$ and a key $r$, when


$m$ and $r$ are elements of $\mathbb{Z}/n\mathbb{Z}$, the additive group of integers modulo n, or when
$m$ and $r$ are elements of a group $G$ isomorphic to $\mathbb{Z}/n\mathbb{Z}$.


Such groups would be a natural choice to implement an OTP. 

There are however also other possibilities. For instance one can easily imagine a perfectly secure OTP construction where the key $r$ is an element of a group $G$ and the message $m$ is an element of a subgroup of $G$. (The key is then larger than the message).

Now, lets come back to your constructions. In both constructions you assume $r,m\in \{1,...,n-1\}$ using the unconventional notation $r,m\in(0;n)$.


Construction 1: You compute $c=r\cdot m $ mod $n$. If $n$ is a prime, then you have the multiplicative group of a prime field and it will work. As you already found out, it will not work when $n$ is composite.
Construction 2: You compute $c=r+ m $ mod $n$. It would be perfectly secure if you had $\mathbb{Z}/n\mathbb{Z}$. However, since you exclude the 0 element, you know that you always have $m\ne c$, and it is thus not perfectly secure. :)