Seems like 1/3rd is more or less right. I think you're underestimating how big enterprise buy-in for the G-Suite is, Docs and Sheets are both widely used at this point.
I do wonder what "market share" means here, and how the domains are selected. The massive market share of GoDaddy seems off, especially since from their website they seem to be reselling Microsoft Office 365, but could be explained by default email MX records on domains registered there (do they do that?).
Don't forget that GoogleApps/Gmail (and google classroom) is also rather popular in education.
Given: thickness of paper 0.0039 inches Lets say each email is at least a page
0.0039 inches * 300*10^9 pages to km = 29,718 (km)
Maybe if some emails are more than a page its not too far off.
> More than 300bn emails are said to be sent every day and if only one-third originate on Gmail—a conservative estimate—then a stack of print-outs would be 10,000km high.
I don't think that's a conservative estimate at all. In fact, I'd say it's a massive over-estimation.
Only one type of email is dominated by Gmail: personal email. I don't know about everyone, but I don't see many personal emails being sent.
Lots of those emails are for work, and there Gmail is not dominant at all. It's not insignificant, but Microsoft is a significantly larger part of the pile.
Another very large part of the total is automated emails, which are not sent through Gmail either.
Since Google Cloud doesn't include an email service, I'd go so far as to guess that more email originates from Amazon (SES) than from Google.