Digital Rights Management, or DRM is actually a way to prevent copying of material, whether it is computer code, a Movie, or other item.
Some of it is rather unobtrusive (for example, most of Sony's Playstation games have a form of DRM attached to the disc and the console) whilst others are very obtrusive (example, STEAM where you have to download something outside of the material itself in order to have the material run).
CD codes do NOT prevent copying of the code, and many disks can be copied that have CD codes to install.
Copy protection also does not equal DRM. DRM is specifically meant to control access to digital material, and grant rights only via an accepted source...typically either by some form of code on the disc or music itself (for example mp4 is different than m4a in that the p stands for protected). Ironically, mp3s and mp4s now are not so protected and the P doesn't exactly seem to stand for what it used to stand for in Apple Products.
DRM, as per the actual copy protection that extends to electronic means to restrict one from the actual copying of code, movie, or other material is considered illegal to circumvent in many nations. If you circumvent it, even if you have bought and paid for the product, it is actually an illegal act in many areas of the world.
Intrusive DRM, as opposed to non-intrusive, typically forces the user to do things beyond simply accessing the material to utilize or view. In these cases, it may install unwanted programming, force access from another program, or cause one unable to view the material on certain machines due to the format to prevent copying on those same machines, or to prevent reviewing or downloading (streaming from many sites would fall into these categories, where you can watch the stream, but they put DRM in order to prevent it from being downloaded/copied to the machine it is viewed on).
DRM was generally accepted by the public in the past, however as DRM got more intrusive, and sometimes damaging to machines, you start to see pushback against DRM. DRM in the music industry has been utilized legally to steal music by the corporations from the actual artists, to rob the actual creators of material so that businesses can own the rights and prevent release, as well as other nefarious acts. It also has been used to install malware, backdoors, and other items onto computers where it was unwanted. Steam got a bad reputation originally because it was NOT forthcoming and open about being needed to install in order to allow games to also be installed.
After a bunch of angry gamers protested, boxes started to have "internet connection required" under the requirements section, and later, since people were still upset that even with an internet connection, STEAM was installed against their wishes at times, that it was necessary to install STEAM in order to install a game.
I personally don't like intrusive DRM because it installs unnecessary items simply to run a game. There is almost NO game on STEAM that actually requires STEAM to run. Hence, STEAM is an unnecessary and obtrusive product that really serves no purpose.
Many people these days simply do not care about things like this, for example, they'll easily give away all their personal information for a free app on Android, or let companies get their personal info via the net on social media.
Other people want their privacy, or want more control over their systems (for example, windows 10 allows FAR less control over your computer than Windows XP did, and many who want more control use Linux or other programs instead of Windows 10).
It all basically boils down to what one wants. At it's core, DRM is digital rights management, meaning it has to be a digital product and it deals with the RIGHTS of the product (so that normally is in regards to copying the product or the ability to have the product copies, do you have that right or what rights in that regards will it allow in regards to download, copy, and utilization).
DRM could be considered applicable if you cannot play online without authorization from the Rights holder. It would not be considered applicable in regards to the company if it is simply a matter of accessing it via a password...as a password could be considered YOUR rights in regards to privacy on a personal account. In this manner, Microsoft can say you need an account in order to use their product, and their DRM therefore would be the needed seed from their server, but that actual account you need is a personal item directly for you which means it is YOUR protection (so I suppose your DRM for any digital material you have on the account.
I don't see CD keys as DRM any more than I see a simple CD check (seeing if something is in the drive) as DRM. I see something on the disc that prevents copying and may interfere with it's being played on certain systems as possible DRM, and definitely consider a program that requires an internet connection in order to play it at all and hence prevent any copying...definite DRM.
DRM free means that you are free from these types of Digital Rights management, that you are freely able to copy the code and keep it with you without the rights holder being able to withdraw that right, or stop you from copying at their leisure or design.