It would be highly unfair if it got overlooked on those grounds.

It was unmanned. Their final goal is to launch a human into space.

Hence why I wrote 'would' and not 'does'. My question is if it counts once they actually manage.

I'm not sure how doing manned suborbitals would stack up against Japan's JAXA which semi-regularly puts things into orbit: https://en.wikipedia.org/wiki/H-IIA#Launch_history

They don't have active plans for manned missions right now iirc, but I would venture to guess that if they wanted to, they could put someone up there without too much effort. The most immediately obvious hurdle is that they would need a human-rated pressurized reentry vehicle.

Perhaps, but the record is to put a human in space. The Soviets won most of the space race, because they did most of the milestones first. In the terms of race; Denmark could beat Japan if Japan never puts a human in space beforehand.

Of course, saying 'Denmark' in this context seems a bit weird, as it is not our government pushing it, but volunteers. But I will admit it does make me a little proud to be Danish. One of those few times.

I'd say it would make Copenhagen Suborbitals the 4:th entry on the list. Much more impressive, since it isn't backed/funded by a government.