Being in the same business does not make it trademark infringement. Ubuntu could also advertise "This OS can run software for Windows by using WINE" without infringing on Microsoft's trademark, because they aren't acting under the trademark. Trademarks exist so you can't sell your product under the established name of another company and profit from their reputation or ruin it by selling bad products. Just mentioning the name to state a fact is not forbidden. Just writing a driver and distributing it with the claim "HDMI-compatible" is not trademark infringement. They problem in OP's article is that AMD has a contract with the HDMI Forum.
Do you think it would be trademark infringement if I code a HDMI driver and then publish it on GitHub with the description "This is a HDMI-Compatible driver"?