In the event that the vote calculation is new to anyone else (it was to me), it looks like this [1] is what they are doing
However, I would claim that with a list of 8 options it is close to impossible for a human to come up with a stable ordering. If you were to vote 3 times or 5 times without being allowed to look at your previous ballot sheets, how much would the votes change?
(I hope what I mean is clear, if not feel free to push me for clarification)
Intentionally or not you've performed a little bit of sleight of hand. At first our voter doesn't care which of "most of them" gets chosen, they've no preference. Then one of these gets picked and "it can matter".
But it doesn't matter to the voter we're thinking about at all. The people "it can matter" for thought hard about this option because it mattered to them by definition, and so their sincere preference was incorporated into the decision.
By smuggling their preference back in as a concealed preference of other voters who didn't actually care, you inflate their position. If I say I don't care between Pizza and Burgers, and then Burgers win, you don't get to count me as a secret supporter of your "Let's eat these stale Doritos I found" faction just because you feel my support of Burgers ought not to really count.
To steelman a bit, let's consider a worst-case brute force manual tabulation of the results (there certainly may be more efficient ways to do it by hand than what I write here):
On a ranked ballot with 8 proposals, there's effectively (8 * 7)=56 binary options (do you prefer A over B, do you prefer B over A, do you prefer A over C, etc.)
In this vote, there were 452 valid ballots. 452 * 56 = 25,312 individual data points to tabulate, into a 8x8 matrix of results. If reading an individual result off a ballot and counting it takes a person 1-10 seconds, the entire tabulation would take 7-70 person-hours.
With that 8x8 matrix of individual results tabulated, determining the Condorcet winner (or the members of the Schulze set, if there's no Condorcet winner), takes less than 1 person-hour, by hand.
Now, that's certainly not an instantaneous result, but it's certainly within the realm of feasibility for a completely non-electronic election or referendum.
As another way of sanity-checking, consider that major elections in the U.S. often involve a combination of local, state, and federal ballots that can have upwards of 30 individual questions in total, and millions of ballots are cast, and results are typically certified within a fairly short timeframe.
It offline's certainly the case that an all-electronic vote is faster, more convenient, and that this lower cost can also allow for more proposals on the ballot, and more frequent and more granular elections, but I'd say it's a far cray from being "absolutely dependent on electronic vote".