Hardness of Short Interger Solution in lattices
No, we cannot say that Short Integer Solution ($SIS$) problem is NP-Complete.

The results from those two papers are not directly related like that, because on the first one, the reduction is from $SIVP_\sqrt{n}$ to $SIS$ while in the second paper, $SIVP_c$ is proven to be NP-Hard for any constant $c$.

Until now, there is no proof that $SIVP_\sqrt{n}$ is NP-Hard and, since it has been proven to be in the intersection of NP and coNP, researchers believe that it is not NP-Hard.