It's a multi-entry visa. A multi-entry visa is multi-entry, with no additional fees, for the duration of the visa, that is how they work. The price is stated, 10,000B. Other examples would be the METV, Elite, or the non-immigrant "O-X" retirement visa, these are all multi-entry and work the same way, multiple entries for the life of the visa.
You need a re-entry permit with either (1) a single entry visa or (2) an extension of stay which is what most retirees are on. An extension of stay is not a visa. If you were on a multi-entry visa like the O-X, you would not need this. That you personally need a re-entry permit just means you are not on a multi-entry visa. It doesn't mean they don't exist.
This is a visa, valid for five years, and is explicitly multi-entry.
As for eligibility, I'm sure there will be eligibility criteria. It's entirely possible the eligibility criteria will be ridiculous, they have form with this. But none of this has anything to do with whether it's a multi-entry visa, which was your issue with "It doesn't say anything about this being a multi-entry". In fact it does, as confirmed by the MFA.