Is there a name for this property of a term rewriting system?
I'm not sure there is a name for this specific property, though I would say "All right-hand sides are in head-normal form".

To be honest, this seems like a very strange property to request, especially since an inner reduction may provoke a head reduction, like so:

$$ {\cal R} = \{a \rightarrow b, f(b)\rightarrow f(a)\}$$
(I'm using letters for function symbols instead of numbers, as is traditional). In this case $f(a)$, the right hand side of the second rule, does not match any rule at it's head, but it may match the second rule if you apply the $a\rightarrow b$ reduction inside.