If $M$ is the direct sum of type 1 von Neumann algebras $(M_i)_i$ it is type 1 ,too.
Concerning the proof: First of all, as the von Neumann algebras $M_i$ act themselves on some Hilbert space $H_i$ is ti correct, that the direct sum acts upon the direct sum of these Hilbert spaces?
And more importantly: The author begins to state that there are pairwise orthogonal, central projection $r_i\in M$ s.t. $r_iM=M_i$ for all $i$. Are those given by the elements $(0,\dots,0,1,0,\dots,0)$ with the one being on the $i$-th position?
Yes and yes. An easy way to think about it, is that the unit of each $M_j$ is a central projection, so the central carrier (in $M$) of each $p\in M_j$ is still in $M_j$. So, given any central projection $p\in M$, there exists $j$ such that $q_jp\ne0$ (where $q_j$ is the unit of $M_j$). As $M_j$ is type I, there is an abelian projection $r\in M$; so $rpq_j$ is an abelian subprojection of $p$. Thus $M$ is type I.