The link was changed from the original Nature article which has the original title. The new link is unrelated.

You're correct that the innovation is really about sparse linear algebra (though not just solvers) done in hardware. However the advantages are exploited not just by way of solving linear systems for implicit time-stepping. They implemented a Jacobi iteration in hardware for solving a system arising from discretization of the Poisson equation, but they also used an efficient forward-map of the coefficient matrix to do explicit time-stepping for a wave solver. So they solve both a time-independent and time-dependent problem, but neither with implicit time-stepping (though there appears to be no technical limitation here, it's just what they focused on).