Oh, look, a really long post! I'll make some statements about stuff and then three ways magic could work. Maybe they'll start a train of thought.
Okay, what i meant when i said what i said way back then (ie. a few days ago) is that the people living in this universe would not have a name for it at all. You see, we still have no idea what gravity is, exactly. This does not make us label it "magic". In fact, we don't label it at all. "An unsolved scientific conundrum" one may say, but that is an explanation, not a label.
One may also argue that this is such a large, strange part of their lives, they would notice it and name it. But i would return to my gravity argument. For the longest time, it didn't even have the name of "gravity". It was just incredibly natural that things fall down. And gravity is, after all, a somewhat important aspect of our lives.
"But magic is something they actively make use of in their life, gravity is a natural force", one may also say. But we have, in fact, purposefully used gravity to, amongst many other things, bring fresh water into Rome and tell time with pendulum clocks. At this time, no-one thought twice of it.
Ultimately, it may well be an artisanship, and have a name alongside "woodworker" or "smith". But artisans are classified by what they produce, not what they use - both the woodworker and smith may use a knife in their everyday life. As such, both of they may be able to use some sort of magic in their work, but a spell to light a forge would still be named alongside tools such as "hammer" and "anvil". How people think of it and how the mechanics of using magic are very connected. If it is a very specific and difficult thing to learn, a smith may not have access to it and it may have it's own name. However, if it is common and using a fire spell is more connected to making, maintaining and using fire than using something such as spellcraft, it would probably not have any specific term associated with it.
Alternatively, we may look at the pagan peoples of Europe - the Gauls, Germanic tribes, and later, the viking nations. These people believed in the existence of magic and used it. Things like curses and fertility prayers were completely real to these people. As "magic", they largely explained things they could not understand, which would apply to the magic of a game. But they also couldn't explain things like breathing. To them, the soul was a moving thing. One had to let it out and draw it all the time. If you would keep your soul inside of you for too long, you would die because your soul can't move and if you didn't draw breath again, your soul would stay out of your body and you would die (I do believe that the world "breathe" is inferred from "soul" in the Finno-Ugric languages). As such, in a game, magic could be connected to religion and have things attributed to it that aren't true. Continuing the smith example, he may have a spell to light the fire which he calls something like "magic". But - he may believe that the fire he has lit and keeps hot with coals and an airflow is the same spell, that his spell does not end when the fire is lit. It certainly seems magical, this strange moving thing that can MELT METAL FOR CHRISTSSAKES.
Thirdly, we may look at the myriad of "-logies" of the Victorian era. Sciences that read the shape of the skull and treat people with electricity. Things that we would now consider to have no scientific merit whatsoever. As such, in a slightly steampunkish world, magic could easily be some sort of science or pseudoscience, though probably more likely to be widespread. But i would still imagine that the internal combustion engine and a some ingenious new spell would be treated in similar victorianesque fashion. The creator presents his new invention in some astonishing way, such as the the guy that got into an elevator and had the wires cut to demonstrate elevator breaks or so many other demonstrations of the era. Monocles are popped. Papers are signed. And so on.