Why does Learning With Errors require a bunch of samples?
The number of rows in matrix $\textbf{A}$ shows the number of LWE samples and $m=1$ means the adversary has access only to one sample. This would be a naive adversary model and would not be suitable for assessing the true hardness of the Problem.
To consider a more powerful adversary model, a (seemingly) stronger definition is to assume that the adversary has access to arbitrary $m$ independent samples.

In the case of R-LWE, a single sample ($m=1$) takes the place of $n$ (correlated) LWE samples.
Even if we assume that the adversary has only one sample, then just as in LWE, finding the secret seems (intuitively) to be harder.