Two things.
"The regression models controlled for several covariates: restaurant closures in the mask mandate models and mask mandates in the restaurant reopening models, as well as bar closures,** stay-at-home orders,†† bans on gatherings of ≥10 persons,§§ daily COVID-19 tests per 100,000 persons, county, and time (day). "
This means the modeling was done conservatively. The changes they are reporting are those for which only unique variance from masking is considered. Of course, none of this takes into account cause and effect. So if masking caused variance in any of the control variables, it would suppress the independent effect of masking.
"During March 1–December 31, 2020, state-issued mask mandates applied in 2,313 (73.6%) of the 3,142 U.S. counties. Mask mandates were associated with a 0.5 percentage point decrease (p = 0.02) in daily COVID-19 case growth rates 1–20 days after implementation and decreases of 1.1, 1.5, 1.7, and 1.8 percentage points 21–40, 41–60, 61–80, and 81–100 days, respectively, after implementation (p<0.01 for all) (
Table 1) (
Figure). Mask mandates were associated with a 0.7 percentage point decrease (p = 0.03) in daily COVID-19 death growth rates 1–20 days after implementation and decreases of 1.0, 1.4, 1.6, and 1.9 percentage points 21–40, 41–60, 61–80, and 81–100 days, respectively, after implementation (p<0.01 for all). "
These are changes in GROWTH RATES, not Covid infection rates themselves. So I think this makes the outcome all the more impressive. The analysis suggests the mandatory masking policy retarded the growth rate of COVID in the community, even accounting for all these other factors which have shared variance with the masking.
This is a very conservative analysis. I do not like multiple regression in this context. A better analysis would be something called "relative importance" which looks at the relative contribution of several predictor to an outcome - e.g., capacity controls, mask mandate, bar closures, etc. Almost certainly it would show an even larger effect for mask mandates.