I think part of the argument opponents of this idea are going to marshal involves the precursor to the definition you give:

any of the following acts committed with intent to destroy, in whole or in part, a national, ethnical, racial or religious group, as such: killing members of the group; causing serious bodily or mental harm to members of the group; deliberately inflicting on the group conditions of life calculated to bring about its physical destruction in whole or in part1; imposing measures intended to prevent births within the group; [and] forcibly transferring children of the group to another group.

So it's the "with intent to destroy, in whole or in part, a national, ethnical, racial, or religious group" that's problematic. African slaves were not a single ethnic group. They were not a single racial group (this depends on how you define "race", but it's an invented idea - socially constructed - anyway with no objective basis in reality). They were not a single religious group, and they are obviously not a single national group. So that's the first part. African slaves were too diverse a group of people to subsume into any one of these more closely defined sub-groups.

Second is the notion that the intent of Europeans was to "destroy". Truth in fact, African slaves were a valuable commodity for slave traders, and although there were certainly cost-benefit analyses done regarding mortality rates during the middle passage, it's a mistake to see the high mortality rates on the middle passage and assume that European slavers had no incentive to keep their captives alive - or at least not to actively try to kill them. So while the African/New World slave trade was horrific in every way, it's difficult to effectively argue that the intent of the European slave traders was to destroy the Africans in question, let alone the entire societies from which they originated.

On another note, I would caution against equating the slavery of the Nazis with the slavery of the New World. Both were certainly slavery, but the Nazis practiced slavery as a method of execution - they literally intended to work people to death, and only made them work because, why not, might as well get as much out of them as possible. But death was always the end, slavery was just the means. In the New World, slaves were not supposed to die. Sure, lots did because of horrific conditions, but death was not the goal of the slave owner, just an unfortunate cost of doing business (sad as that may be).