That's because you're running a mod of a six year old game on a five year old graphics card - of course you should be fine. I'm talking about driver support for older cards with newer games, such as The Witcher 3, where some people who spent $500 on a GTX 780 only a year earlier were getting less performance than mid range cards from AMD.

For what it's worth, I tried googling for widespread Radeon problems with DayZ and couldn't find anything on the first page.