There might have been an oversight by someone at the company, but I got the number by doing this
10,000 * POWER(1.09, 10) * 0.0003 * 10 = $71.02
Which is incorrect because the fee will have less value early on (as you have shown in your table) but it gets you to the $71 that they are advertising.
After digging into it some more, Vanguard has cut the VTI expense ratio a few times. Looking at this investopedia article they say that the expense ratio was dropped from 0.05% to 0.04% (and obviously it dropped again from 0.04% to 0.03%). Also in this this blog they say that the overall expense ratio was 0.046%. Doing the same math as you were doing with both of these ratios gives the following
0.04% gives a $60.77 fee
0.046% gives a $70.65 fee
0.05% gives a $70.96 fee (excluding the expense for year 1)
So my guess is Vanguard cut their expense ratio but didn't update this comparison of how little their fees were compared to their competitors.