This is such a famous story, and probably true to a degree. However, there is no mention of Guan Yu playing Go in the original text from Records of the Three Kingdoms (三國志 is a historical book, written in the late 3rd century AD, just decades after this said event happened), and it didn't even specific who was the doctor, just said he was still drinking and eating like nothing. The more vivid descriptions came from the 14th century novelization of the Three Kingdoms - Romance of the Three Kingdoms (三國演義), which was more than a thousand years later.
There are a lot of depictions of this event, since Guan Yu had since raised to the status of divinity in Chinese fork religions, and we can see many art, murals, and wall statues about Guan Yu in his temples or related temples.