Based on what I see on some of our demo networks, the network usage figure on the Organization->Overview is the sum of all traffic over seven days, probably a cached value rather than real time, i.e. updated on some schedule, not when the page is redrawn.
You could use https://developer.cisco.com/meraki/api-v1/#!get-network-traffic with timespan set to 604800 then simply sum the sent and recv for each application.
Note that this call requires traffic analysis with hostname visibility to be enabled on the network(s) you want to get data for.
I just tested it on one of our lab networks...
Sum of API data 48,986,330 KB
Figure in overview 46.84 GB, it's lower, but if it is a cached value that would be expected.
Btw my experience is that trying to externally match figures displayed by orchestrator screens (not only Meraki) is often futile...
i) The orchestrator is unlikely to be using the external API, nor the basis of internal calculations publicly documented.
ii) The orchestrator may not be showing the correct numbers anyway! There's a non-Cisco orchestrator that has been misreporting traffic for years, by huge amounts, both in its user interface and in what is accessed via API, it took a while before the vendor accepted our evidence, even longer to find the cause and fix it.