The election of the Doge was an incredibly complicated process, refined across the centuries. It seems to have reached more or less its definitive shape around the fourteenth century, although it was tinkered in minor details up to the end of the Republic. What follows is the description of the election procedure in Maranini's La Costituzione di Venezia, vol. 1, pg. 187-190 (my translation). It is a long passage, but I don't know if a detailed description of the procedure is available in English so I will include it almost in its entirety.
No one having less than thirty years [...] could participate to the [Maggior] Consiglio session for the dogal election. The assembled members were counted and as many ballots as were the present members were put in a cup. In thirty of those ballots there was a cartouche on which it was written the word lector.
A roll call was made; and everyone, when his name was called, approached the urn, from which a boy, monitored by the members of the Signoria, extracted a ballot. All those who had received one of the marked ballots, retired in a nearby room, waiting for that first electoral operation to be over.
Then 30 ballots were put in an urn again, nine of which bear the indication lector. Those who took those nine ballot in the new sortition remained, while the others left. Then the third election took place, almost at unanimity. The nine nominated 40 electors, each of which must have received at least seven votes.
Everyone returned in the main room, where the names of the forty were read that, again with the system of sortition via ballots, were reduced to 12.
The twelve elected 25, each of which must receive at least eight votes. A new sortition reduced the 25 to 9. The nine elected 43, of which each must receive at least seven votes. A new sortition reduced the 43 to 11. The eleven finally elected the forty-one electors of the Doge, each of which must receive at least nine votes. The forty-one elected the new Doge, not though by a simple majority, but with a minimum of 25 votes.
[...] Assembled, the 41 electors nominated a presidency composed of three priors and two scribes. Again a roll call was made and everyone threw his form in an urn monitored by the presidency. The scribes opened the forms and marked the votes. Then, in another urn, many forms were put, on which all names of those receiving votes were marked; and one of this forms were extracted. If the person so designated belonged to the conclave, he must immediately leave. Then the discussion began: and everyone could speak against or in favour of the candidate. If he was one of the electors, he could be recalled to defend himself from the accusations.
At the end of this debate, a new votation proceeded: every elector received three ballots (of different colors, meant to indicate the votes in favour, against and uncertain or insincere). Every elector threw then one of the three ballots in the pozzolo, an urn with three compartments. The count was made; and if the candidate had reached the 25 votes in favour he became doge. Otherwise, the discussion reopened with another name randomly selected like the first; and the procedure was repeated, until a candidate had reached the prescribed amount of votes.
As you can see from the description, it seems that the passage in the question refers to the last step, when the painstakingly selected conclave finally votes for a Doge candidate. However, this is not an example of range voting: as you can see, the candidates were voted in random order, and the first to receive 25 votes in favour was elected, independently from if there were some other candidate that could have received more votes.
The case reported on the website where two different candidates received the same number of votes was indeed historical, but it happened in 1229, where the electoral procedure was different (the previous and following century were a period of constitutional reforms), and the above method was fixed only in 1268, possibly exactly as a reaction to the contested Tiepolo vs Dandolo election. In fact most of the constitutional framework of Venice was explicitly engineered to dampen civil strife, which was endemic and very violent up until the thirteenth century. This worked admirably, and the almost complete lack of civil strife in the following centuries is one of the possible reasons why the Republic of Venice was called the Serenissima (the "most serene").
Since there seem some confusion about what the "insincere" votes mean, let me add another paragraph from Maranini's book about them:
[The uncertain ballots] are not to be confused, as Besta remarks, with what today we'd call abstained. The concept of abstention was incompatible with Venetian public law, where everything had a character of necessity and every right was a duty. The 'uncertain' vote expressed the opinion that a topic was not sufficiently clarified and that it was needed then to procrastinate the decision. However, one understands well how in the political practice often the uncertain vote, as the modern abstention, was a convenient refuge for indecisiveness and cowardice. This is confirmed by the fact that it was admitted in elections, where it was neither opportune nor possible to procrastinate the decision.
My understanding from that was the the 'uncertain' votes were rather votes to prolonging the discussion rather than what today we would understand as abstentions. However this does not mean that they wouldn't be used tactically in a similar way.
