What you say is mostly true, however, those other properties are typically a tiny portion of the total numbers, in most cases, 99% of the total numbers are coming from Google’s SERPs.
There are other plausible reasons that you are seeing the results you indicated. Let’s do the math, shall we?
Not all searches result in a click-through, on average only about half of all searches will receive a click so when we apply that to your 3600 searches here’s what we get:
3600 searches = 1800 clicks.
The #3 position gets about 12% of those clicks on average so that means:
1800 * 0.12 = 216 clicks per month.
We divide that by 30 days in a month:
216/30 = 7.2 visitors per day.
Now if the keyword has commercial intent tied to it then you are likely to have sponsored results that often take more than half of those clicks bringing the average number of daily visitors to about 3.5, and that assumes that you have a great title and description for your listing or it could be considerably lower, maybe 1 a day.
Of course, these are averages and some keywords vary a great deal from the averages so you might see more, or even less. The bottom line is that 3600 searches aren’t all that great of a number. It’s okay if you hit number one, have no strong PPC competition, have a killer title and description in your text snippet, and an above-average CTR. You might get dozens of visitors a day, but that’s a lot of ifs.