Yeah. They were referred to as dwarves in Arena/Daggerfall. Hell, back then there were probably referring to the generic short, bearded, alcoholic, Scottish type. But then Morrowind added in "proper" dwarves and they just retconned previous games, so that "dwarf" was the standard term the Imperials gave the Dwemer. Those Imperials do that all the time anyway, uncultured fools.
That's also true, a lot of the less generic aspects of lore were only added later in the series. At the start, it was pure generic high fantasy, after some retconning and fleshing out of the lore it developed into what it is now.
Maybe in Cyrodil they aren't too concerned with the proper name of a dead race who apparently have no ruins in that part of tamriel, but in morrowind the authorities are more aware of the Dwemer due to history and ancient landmarks that they name them properly.
In Morrowind the name "dwarf" often crops up too, but the Dunmer, of course, tend to use the elven name, and the scholars and collectors who would be interested in Dwemer artifacts probably do their research, so they'd know the name.
No-one was arrested because of it, and trying to enforce it was a waste of money.
I'm pretty sure of at least one peace of evidence of it being enforced, namely the Thieves Guild quest where you were supposed to free a Thieves Guild member in Pelagiad, you did this by stealing a Dwemer artifact from the local trader, and threatening to reveal the fact that one of the legion members takes bribes to overlook the fact that he sells such things unless she frees your guild mate. I think that bribing someone to overlook trading in illegal items would be rather pointless if it isn't enforced anyway.
Not having illegal items such as those was one of Oblivion's flaws, although it was a flaw of Morrowind's that it didn't carry it through very well, other than skooma.
The way skooma and moon sugar were enforced was flawed in Morrowind too, most merchants would not only refuse to buy them, but wouldn't do business with you at all if you had hem, this might seem alright, until you consider the fact that all you had to do was to drop your skooma and moon sugar on the floor to trade with them again to work around it (you'd still need to find a merchant who doesn't mind it to sell the illegal items, of course, but that's not hard. Why they didn't care about other goods in which trade is illegal I don't know.
Actually, I seem to recall community speculation that part of the reason for the change was to explain how armor designed (and therefore fitted) for dwarves (as in the short kind) were somehow being easily worn by human/elf sized people. This was a LONG time ago (possibly before Morrowind was even out), so I'm not sure.
I could believe that one, since armor designed for your typical dwarves that fit the name fitting on human or elf sized characters does have questionable logic, and it's certainly easier to believe than Bethesda doing it just to be original.