Technically maybe.
The thing is though, that languages, tone, understanding and culture is a incredibly complex subject and it's sometimes hard to wrap your head around what is a grey area, and what is outright yokel racism.
Language that is either antagonistic, prejudicial or discriminatory towards a person or community based on either race or ethnicity is defined as racism.
So I don't know if Jamaicans eating goats has some negative connotation has any negative associations outside of Jamaica but if it did then that could certainly be used in an antagonistic way. It's also entirely possible that the language can be used in jest, with a understanding from both sides that there is friendly banter going on.
For example: How many Swedes does it take to change a lightbulb? 20. 1 to hold the bulb and 19 to turn the house around. Swedes are dumb - Love from Norway. Mocking a whole ethnicity for their lack of awareness is generally frowned upon, but in this case its a cultural thing where everyone accepts that this is both fun, and factual. Especially Swedes. If they could read.
Eating dogs is a very negative stereotype towards asians, so the moment you mention it you're antagonistic and prejudicial on purpose. Ie. you're being a racist.
For reference: Ethnicity is defined as a belonging to a social group with a common cultural and/or nationality, not just skin color or physical appearance.