Importance: not really important to read this comment
Update: I updated; see my reply
GivingMultiplier's description according to the EA newsletter^1:
Let's assume Effective_Charity and Local_Charity.
If you were going to give 100 USD to Local_Charity, but instead donate 10 USD to Effective_Charity and 90 USD to Local_Charity, GivingMultiplier will give 9 USD to Local_Charity and 1 USD to Effective_Charity, so there's now 99 USD going to the Local_Charity and 11 USD going the Effective_Charity. GivingMultiplier would give the money to Effective_Charity anyway. So for the donor, this is indistinguishable from donating 99 USD to Local_Charity and 1 USD to Effective_Charity, but it's done in a more obscure way.^2
Also, sure they are rather transparent about their process – at least in the newsletter; it wasn't obvious from the main page of the website –, but still, their scheme mostly works only insofar as people don't understand what's going on.
A bunch of people don't know Why you shouldn’t let “donation matching” affect your giving, and so they will be misguided by donation matches. If EA charities don't use them, then they might be at a disadvantage. So their reasoning might be that the game theory favors also using this technique under a consequentialist moral framework – sort of like a tit-for-tat with other charities, with deceiving donors as an externality.
One could argue that they should link to the piece against donation matching on their website, but maybe both memes are fit to different environments – maybe it would mostly reduce how much people use that specific service to fill their donation matching need, or something like that. I don't know, I'm trying to steelman it.
They might also want to know where people donate money, so they allow people to choose where some money goes among those 9 charities in exchange for knowing where they donate the rest of the money. And at the same time, they signal support for those 9 charities.
Consequences on the donors
If donation matches don't change how much donors give, but just where they give (which seems plausible to me), biasing them equally against all charities might actually help them make decisions that are more aligned with their worldview than if they were less biased with only a subset of them.
1) There website is actually giving different numbers, but the idea is the same.
2) Sure, there's the real choice of choosing which of the 9 Effective Charities receive the money, but:
a) The part about local charities is a red herring
b) Those charities probably sort-of have reached market efficiency (in the sense that large donors can rebalance their donations according to how much total funding they want each of them to have)
(a) is my main objection.