Placement of Vias to Connect Ground Planes
The layout you showed looks like what's called copper-backed coplanar waveguide (CBCPW). That means the ground return for the waveguide is not just in the coplanar grounds (the ground fills on the same layer as the signal traces) but also in the plane layer immediately "below" the signal layer. This structure is fairly esoteric, in the sense that I've only seen it used in digital systems when data rates exceed 20 Gb/s. 

I found what looks like a reasonable discussion on the differences between CBCPW and microstrip in a Microwave Journal article by Rogers Corp engineers. 

This article shows that the CBCPW has lower loss than microstrip at frequencies where radiation loss becomes important in the microstrip, roughly from 25 GHz and up, which explains why CBCPW is not widely used at lower frequencies.

Addressing your question, the article points out some special requirements for grounding vias in CBCPW structures: 


  For proper grounding, CBCPW circuits employ vias to connect the top-layer coplanar ground planes and the bottom-layer ground plane. The placement of these vias can be critical for achieving the desired impedance and loss characteristics, as well as for suppressing parasitic wave modes.


This basically means that without frequent stitching vias between the coplanar ground and the backing ground, power could be transferred to undesired propagation modes, which would cause either excess insertion loss or strong dispersion in the transmission line characteristics.