Why every access structure is a multipartite access structure?
From p5 of the paper:


  An $r$-partition $\Omega = \{P_1,\ldots,P_r\}$ of a set $P$ is a
  disjoint family of non-empty subsets of $P$ with $P=P_1 \cup \ldots
 \cup P_r$. ... A family of subsets $\Lambda \subseteq \mathcal{P}(P)$
  is said to be $\Omega$-partite if $\sigma(\Lambda)=\Lambda$ for every
  permutation $\sigma$ such that $\sigma(P_i) = P_i$ for every $P_i \in
 \Omega$.


Thus any access structure $\Lambda$ on $n$ parties is trivially an $n$-partite access structure: take the $n$-partition $\Omega = \{\{1\},\ldots,\{n\}\}$; then for any $\sigma$ fixing all sets in the partition (which is only the identity permutation), it holds that $\sigma(\Lambda) = \Lambda$.  Since $\Omega$ contains $n$ partitioning sets, $\Lambda$ is an $n$-partite access structure.

The abstract also says that Shamir's scheme is unipartite.  This is by taking the partition $\Omega = \{\{1,\ldots,n\}\}$, which is a $1$-partition, since for every permutation fixing all sets in the partition (which is every permutation) it holds that $\sigma(\Lambda) = \Lambda$.  This is because of the symmetry in Shamir's scheme: every party can be swapped with any other party and you still have "all subsets of $\{1,\ldots,n\}$ of size at most $t$".