The startup rate has been falling for decades:

In a new report from the Brookings Institution, economists Ian Hathaway and Robert Litan offer two partial explanations: population growth and business consolidation.

How does population growth hinder startups?  Seems more likely to be correlated with other causal factors than to be causal itself?  Or are they just talking about the 'rate', meaning we have the same number of startups as before, just more people?

Yes, they're talking about the population growth rate, so yes it's same # of startups but more people.

This is (poorly) illustrated in the chart atop this page.

Overall population growth, however, has been gradually slowing over the past 20 years, possibly dragging the startup rate down with it.