A short explanation for people not trained in group theory:
A group is a set $G$ with a binary operation $\circ$, i.e. for each pair of elements $g\in G$ and $h \in G$ you have $g \circ h$ being again an element of $G$. And furthermore, this group operation needs to fulfill some properties like being associative (i.e. $f\circ(g\circ h)=(f\circ g)\circ h$), there needs to be some identity element $e\in G$ (i.e. $e\circ g=g\circ e =g$ for all $g\in G$), and there needs to be an inverse, i.e. for each $g\in G$ there is an $h\in G$ such that $g\circ h=h\circ g=e$. And with those few and simple requirements you can prove already a whole lot of nice and useful theorems.
A general group does not have to be commutative, i.e. $g\circ h$ is in general not equal to $h \circ g$. Such non-commutative groups we usually write in a "multiplicative" way, that is we write the group operation $\circ$ as multiplication. So we write $gh$ instead of $g \circ h$, we write $g^{-1}$ for the inverses, and we often write $1$ for the identity element.
In contrast, if commutativity holds (i.e. $g\circ h=h\circ g$ holds for all $g$ and $h$ from $G$) we often (but not always) write the group in an "additive" fashion, i.e. $g+h$ for the group operation, $-g$ for the inverse and $0$ for the identity element. The reason for doing it this way is, that addition is always commutative, while multiplication often is not.
The elliptic group is a commutative (also sometimes called Abelian) group, thus often written in this additive fashion. But here you also have to note that point addition in an elliptic curve is not normal geometric point addition, but this strange group operation defined by intersecting the straight line through the points with the curve and mirroring the result at the $x$-axis. And further the zero (identity) element is the "point at infinity" and $-P$ is not the "normal" geometric mirroring at the origin, but mirroring at the $x$-axis. The symbols $+$, $-$ and $0$ are only used here, because the group has this commutative structure.
People could just as well have chosen to write the elliptic curve group in a multiplicative way, with $\cdot$ for the group operation, $g^{-1}$ for the inverse, and $1$ for the identity. There are even ways people talk, where this multiplicative notion still comes out, especially when it comes to the discrete logarithm problem. In a multiplicative group its about finding some integer $k$ that fulfills $g^k=h$ for given $g$ and $h$. In an elliptic curve group its about finding $k$ such that $kP=Q$ for some given $P$ and $Q$, but both are essentially the same: $g^k=g\cdot g\cdot\dots \cdot g=g\circ g\circ\dots \circ g$ vs. $kP=P+P+\dots+P=P\circ P\circ \dots\circ P$. In both cases its just $k-1$ times the application of the group operation and you need to find that $k$.
And whether you call that group operation now $\cdot$ or $+$ is just a matter of personal preference or history or common usage in your community or whatever.
For elliptic curves the nowadays standard seems to be to call the operation "point addition" while the authors behind the paper you cite prefer to use multiplicative notation. An advantage I can see in this, is that this is more in line with cryptographic algorithms that are based on modular arithmetic where multiplicative notation prevails (and where the notion "discrete logarithm problem" makes much more sense, cause in additive notation this is much more of a "discrete division problem"...)
