I have thought of loops as having the operations of multiplication and left and right division. I read the D. R. Hughes article on Additive and Multiplicative Loops of Planar Ternary Rings and it contains:
We define addition in $R$ by $a + b = F(1, a, b)$, and multiplication by $ab = F(a, b, 0)$. Then the set $R$, under addition, forms a loop with identity $0$, and the set $R^*$ of nonzero elements of $F$, under multiplication, forms a loop with identity $1$ ... These loops are called the additive and multiplicative loops, respectively.
The article seems to build a ring from the loops and a set with multiplication and addition defined for it fits with my understanding of rings. I have searched for "additive loop" and found it used in many articles though none have clarified my understanding of the term "loop" as addition relates to it.
A loop is a set with some binary operation on it which satisfies some axioms. That binary operation is usually called "multiplication" but that's just a name. In particular, it's perfectly fine to instead call it "addition" if that makes sense in a certain context. So, that's all that's going on here: there is an operation called "addition" on the set $R$ and we're using it as the operation for a loop structure on $R$. We then refer to this loop as the "additive loop" of $R$ to distinguish it from other loop structures we might have relating to $R$.