The only requirements are that you
1) have a Swedish bank account that supports the service (not all banks do), and
2) have Mobilt BankID on your phone.
If you possess a Swedish bank account and are in the Swedish Population Register, you should be able to get Mobilt BankID on your phone (which is, like Swish, an app available on the App Store everywhere) with your Internet bank and then set up Swish.
That sounds like it makes it impossible for any other phone OS to enter the Swedish market.
You need the app to be able to send money though (iOS, android or windows phone).
Yes it is stupid. Unfortunately it is convenient, which is enough for 95% of the population.
But there are still, somehow, banks in Sweden which don't support one or the other. And, well, useful as Swish is, it's not actually obligatory for life in Sweden.
For what it's worth, BankID and Swish also support Windows Phone… for the remainder of 2018, anyway.
I have a Swedish bank account, but I still can't use Swish because I have an American phone. It's infuriating.