I have heard that Google includes everything in those estimates, including how much traffic goes through the paid search and content networks. This is why it is a good idea to diversify your portfolio of traffic/ sites/ income methods as much as possible.
Here is the chart for percentage of total estimated searches (by position in the SERPs):
Page one:
Position 1: 30%
Position 2: 15%
Position 3: 7%
Position 4: 5%
Position 5: 4%
Position 6: 4%
Position 7: 2%
Position 8: 2%
In this case, Vini's site listed in the example above SHOULD be getting approximately 4,200 hits per month, or roughly 140 hits/ day. The fact that on some days he (or she) gets zero means that Google is using other data to calculate their total.
Do a backlink comparison to see who is outranking you, then try throwing some backlinks at the problem, maybe some PPC to get the site up and over. I have seen this work. Also-- you didn't mention if this is an exact-match domain? That sometimes makes a difference.