Most western countries count a death as COVID-19 if COVID was a contributing factor - in short "but for COVID-19, the person would still be alive".
These become ethical issues as we saw with the outcry over the comment by a governor (IIRC) that "these people would have been dead in six months anyway".
A different example is Alzheimer's. If my dad didn't have Alzheimer's then he probably wouldn't have gotten a colon problem that required surgery and resulted in getting MRSA. Without MRSA he wouldn't have gone into rehab, gotten an infection that resulted in an amputation, that caused him not to be mobile and to get recurring infection that ultimately killed him. The same holds true for COVID-19. Nick Cordero is a prime example, sick since the beginning of April, leg amputation, severe lung damage and so forth. But for COVID-19, he wouldn't be in the hospital but he likely die from some other cause.
I'm not sure what China, Russia and Iran are using as criteria, but it certainly isn't "but for".