Science fiction book about an entity feeding off of war

"Unnatural Causes" from Callahan's Crosstime Saloon?

Callahan's Crosstime Saloon by Spider Robinson was published in 1977, so the timeframe matches even though the author is Canadian-American. The book is made up of several stories all set in Callahan's Bar.

The first story in the book "The Guy With The Eyes" deals with a cybernetic alien who visits Callahan's Bar and confesses that he has been sent to scout the Earth and report back to his Masters. The regretful alien is certain that his report will result in an immediate order to destroy the Earth, so he offers to lower his otherwise impenetrable defences in order to let the humans kill him and save their planet - his defences are under his control but the cybernetic components that will send the report are hardwired beyond the alien's control. Callahan, his patrons and the alien, now named Mickey Finn, come up with an alternative that results in the alien surviving and remaining on Earth but the report is not sent. For the purpose of the question, this story is merely background to...

In "Unnatural Causes", a costumed Halloween party is happening at Callahan's Bar and Mickey Finn comes to visit. Finn realises that one of the patron's alien appearance is not a costume when he notes that they are both using their infrared-spectrum vision to watch heated air currents over the fireplace. The alien admits that he is part of a team that have been nurturing wars, rapid technological development and dysfunctional societal development as part of his race's 2000 year scheme to have all humans kill each other. Once the humans have killed each other, the alien Krundai will feed on them. (The Krundai are squeamish about killing but not about eating.)

However, this is where events diverge from the OP's description - the Krundai individual who has visited the bar leaves and violently commits suicide in the car park, then Mickey Finn hunts down the remaining Krundai covertly, resulting in a number of small, unexplained earthquakes around the world. Finn is not killed by the humans, he returns and plays a significant part in some of the later stories published in other volumes.

Not so much feeding off war, but making a profit on it, which should allow the aliens to purchase sustenance is one of Larry Nivens Draco Tavern stories, "War Movie"

In it we are told of how alien explorers had happened across Earth during WWII and recorded several battles, including the A-bombs at the end and made a huge profit off them. In the story's current time, things weren't going so well, as the follow-up alien expedition found peace had broken out, so there was nothing to record for profit off of. They were going bankrupt. There was some in-story speculation of what might happen if the aliens bribed some nation to start trouble.