The difference to tabulating IRV votes is that for Expanding Approvals, knowing the total number of 1st, 2nd, etc. rankings for each candidate fully suffices to calculate the election winner, since approval counts are not dependent on higher preferences being eliminated.
The EC would have to sum the number of 1st-, 2nd-, etc. place-preferences for each of the candidates (the Election Management Portal seems to already collect this information), and then add the approvals from previous rounds and the new approvals from the ranking corresponding to the current round for each candidate in each round. In the spoiler below, I’ll explain it with a concrete example, if this is a bit too abstract 
Example
(These are the real numbers from the July 2022 MoC Special Election, which was the only multi-candidate election that didn’t end after the 1st round that I’ve found)
| Candidate | First-preference | Second | Third | Fourth | Fifth |
|---|---|---|---|---|---|
| Comfed | 3 | 6 | 7 | 1 | 1 |
| Murelia | 3 | 7 | 4 | 2 | 2 |
| ProfessorHenn | 7 | 4 | 1 | 6 | 1 |
| maluhia | 7 | 2 | 5 | 3 | 0 |
| RON | 0 | 1 | 1 | 5 | 8 |
From the numbers alone, it’s not possible to deduce the IRV winner, since there’s no indication which of the second-place preferences represent e.g. the three Comfed voters’ second choices - each round will need a renewed examination of the relevant ballots to know where the votes will ultimately transfer to.
Under Expanding Approvals however, it doesn’t matter who a voter’s higher preferences are when tabulating a round’s totals - a voter approves all their top preferences for the respective round, independently of any condition like a higher preference being eliminated. This makes it relatively quick to calculate. For the above example, we’d get the following approval totals:
| Candidate | Round 1 Approvals | + 2nd-place preferences | = Round 2 Approvals | + 3rd-place preferences | = Round 3 Approvals |
|---|---|---|---|---|---|
| Comfed | 3 | 6 | 9 | 7 | 16 |
| Murelia | 3 | 7 | 10 | 4 | 14 |
| ProfessorHenn | 7 | 4 | 11 | (1) | (12) |
| maluhia | 7 | 2 | 9 | 5 | 14 |
| RON | 0 | 1 | 1 | 1 | 2 |
Since we have 20 voters, the election threshold would be 11 approvals. For a two-winner election like the Delegate one, this would mean that Henn (I swear this is just a coincidence 
) would win the first spot in the second round, and Comfed would win the second spot in the third round (theoretically, Murelia and maluhia were above 11 too, but I’ve broken the tie in Comfed’s favour since they received more approvals overall).