No, it's *not* called "The Excruciator" most of the time. There's a total of two times it's mentioned that I count, and it's called "the Excruciator" once, but that's in a context where any device might be called by the definite article. "The most gruesome of these devices was the Excruciator", just like "The most expensive of these dishes was the filet mignon". The other reference very much wants to emphasize the device's uniqueness but uses the indefinite article: "Can you imagine, human, what it must have been like to wear an Excruciator?"
It's not like there's much precedent in English for using the definite vs. indefinite article for simple emphasis anyway. "The" usually means there's one particular member of a group that's important -- not just some guy named Martin Luther King, but *the* Martin Luther King, or not just any house but *the* house (the one that's haunted) or something like that. That makes no sense here; the fact that Excruciators as a class are special is already reflected by the capital letter. Calling the whole class "The Excruciator" rather than "Excruciators" isn't a form of emphasis, it's just stilted.
Also... Kohr-Ah didn't rise to prominence until after the war ended. He didn't invent the Excruciator; most likely a Green Ur-Quan did, since they were the scientists and technologists, though we are never told. The Kohr-Ah seem a lot more hung up about Excruciators than the Kzer-Za -- they're more messed up in general -- but that doesn't mean Kohr-Ah himself played a special role in their creation.
Also... no evidence that the other races even participated in the war, and given that it's called the Ur-Quan Slave Revolt, that all the other races besides the Ur-Quan were almost destroyed, and the fundamental arrogance of the Ur-Quan I somehow doubt they were let in on the whole Excruciator thing.