I am not an expert in this area, and still have to look the paper beyond the first few pages, but find the result astounding. In particular, the common intuition is that since all physical quantities are “nice” function (continuous, differentiable, etc..), we could never distinguish between the case that the universe is infinite or discretized at a fine enough grid. The new work (as far as I understand) provides a finite experiment that can potentially succeed with probability 1 if the two provers use an infinite amount of shared entangled state, but would succeed with probability at most 1/2 if they use only a finite amount. A priori you would expect that if there is a strategy that succeeds with probability 1 with an infinite entanglement, then you could succeed with probability at least $1-\epsilon$ with a finite entangled state whose dimension depends only on $\epsilon$.
The result was preceded by Ito and Vidick’s 2012 result that $\mathbf{NEXP} \subseteq \mathbf{MIP^*}$ and Natarajan and Wright’s result last year that $\mathbf{NEEXP}$ (non deterministic double exponential time) is contained in $\mathbf{MIP^*}$. This brings to mind Edmonds’ classic quote that: