I don't think it makes sense to look at it this way. I would look at it as any other warrant issued by any body. If the target of the warrant lives in a country that recognizes ICC warrants, then it's more or less similar to a warrant issued by that country's government. If not, then it's similar to a country issuing a warrant for the arrest of someone who lives outside their jurisdiction, with no extradition treaties in place.

I do agree that the end result is a sort of "travel ban", but that's no different than if the US issued a warrant for (say) a Chinese citizen living in China. The Chinese government is probably not going to hand that person over, and that person is effectively barred from travel to the US (and likely other countries like Canada that might help the US enforce that warrant if the opportunity presented itself), unless they want to get arrested.