no it doesn't, it literally means the house/room where your wives & lovers live together. which is the custom where the term originates from. one man, many wives.
but for VNs etc. it just means you can get all the women instead of having to choose one.
I would go even further than this. The original Harem was meant for all important female members of someone's household. This included not only wives and lovers, but daughters, distant relatives, household workers, and sometimes even young boys. The term wasn't sexual in nature at all. It was a sacred place where women had more privilege,
modesty, and protection.
Modern civilization saw this, and some started to make assumptions that it was just reserved for lovers. Maybe in some cases it was, we certainly can't poll every wealthy family in history to make this determination. Certainly the JP hentai/ecchi version of Harem is not in line at all with the original Arabic 'harim', because JP gonna perv.
What it means now in terms of porn is up for debate, but I would argue that many of the same original meanings apply.
All important female lovers of the main character having roughly equal status with and protection of the MC, willing to share him equally. Not all females in the game need to be part of a harem, but those that do are clearly ok with the MC fucking any other in the harem, and being together at the same time with the MC.