What makes me know for a fact, not "think" that they are an "international bank" is that I sent money directly there via SWIFT, which is via an MT103 which is an authenticated payment message. So factually yes, they are an international bank with which I've factually received money from one country into another country being Thailand on many occasions. They can also send monies via outward remittance in over 150 currencies. I hope that settles the matter for you.
No, that does not alter the fact that the Thai bank that you referenced is not, factually, an "international bank". That a bank is a member of the SWIFT organisation does not make it an international bank.
Krungthai Bank is, factually, a domestic state Thai bank through which it's customers are able, via SWIFT, to send and receive international transfers, it is not, factually, an "international bank". I hope that settles the matter for you...factually.