The mathematics behind PCA are quite complex, but I find this an excellent explanation.
My rough interpretation is that the most variability in the dataset is projected on these two dimensions, so for genotypes, these are both mostly explained by geographical/ethnical differences. This can also be present in PC3, PC4,... etc. But just the two first components are visualised. And I think your conclusion is correct: populations are equally spread and mixed so no reason to assume population stratification. If the genotypes of the individuals were very different between blue and red cohorts you would expect that PCA separates the two cohorts you can't claim that the samples are from the same population.