That paper isn't robust evidence, it's the kind of joke quality that typifies masks-work papers actually. RCTs are how you try to decide whether a medical intervention works, they're considered the gold standard for a reason.
Problems with this paper:
1. It's just a study of public data so should be trivially replicable, but they picked data points "via Microsoft Excel’s random number generator function" so it's non-replicable by design. Right up front this makes it incompetent work because there'd be no way to detect P-hacking.
2. Because it's not an RCT they can only show a correlation, not a causation, yet their claims are causal. An obvious confounder is that going out with a mask is no fun so you'd expect people to socialize more in places without a mandate, yet this isn't mentioned.
3. The effect size is tiny: ~4 cases a day! In counties with tens of thousands of people! This is NOT how mask mandates were advertised to the population.
4. "We did not record compliance with mask mandates". Yes I'm sure the residents of places like Anderson County Tennessee followed public health orders meticulously.
5. They ignore all the contradictory evidence.
Again, I cannot stress this enough, we know mask mandates don't work because of the times they were introduced with no change in case trends. Here's a single example:
https://pbs.twimg.com/media/FPHy4ZoUYAIsYbt.jpg:large
Because the claim is "mask mandates always reduce transmission", it only takes one counter-example to disprove the claim. There are hundreds of charts like that one, but only one is required. That's the nature of falsifiability.
To conclude that mask mandates work you have to be able to explain the times when they didn't. Crap studies like this one (cited 3 times, well done for finding it) are produced by academia all the time, but they get ignored because they can't explain that, and the authors are invariably biased. These guys even cite a claimed 0.5% reduction in cases and call this "effective"! Imagine if governments had stated up front when imposing mask mandates for the first time, "we think this will be effective because it might reduce case counts by half a percent". What would people have thought of the sanity of this cost/benefit tradeoff, exactly?