@DavePhD's excellent answer reviews the provenance of the phrase at issue. His research suggests that it is a known English phrase that is overwhelmingly used in reference to a paranormal event from New England in the 17th century. The conclusion would appear to be that it is not (or at least was not for a long time) a slur towards Muslims or anyone else.
However, as any student of language knows, context matters. Perhaps, the context in which this phrase is appearing (a Magic the Gathering card from a set called Arabian Nights which was released in 1993) is enough to elevate an otherwise innocuous phrase to the level of ethnic slur. Indeed, it begs the question: What would possess someone designing an Arabia-themed card game to reference a little-known event from 17th century New England? Many people have suggested that the name is actually a derogatory reference to Palestinian "stone throwers" especially given the timing of the set, which was nearly contemporaneous to the First Intifada. Even barring an intentional allusion, the slight towards Palestinians might reasonably be inferred from the context (i.e the Arabian Nights set) since Palestinians generally consider themselves Arab.
These poor optics might be enough to err on the side of caution for a company whose product is under scrutiny; however, I believe that there is further missing context which makes good sense of this card without reference to any pejorative. Specifically, in Arab mythology, djinn are widely understood to throw stones as a way to pester (and sometimes kill) passersby.
This open-access edition of One Thousand and One Nights contains an historical note about djinn, including this observation:
I have mentioned in a former work, that malicious or disturbed Jinnees are asserted often to station themselves on the roofs, or at the windows, of houses, and to throw down bricks and stones on persons passing by. When they take possession of an uninhabited house, they seldom fail to persecute terribly any person who goes to reside in it.
The translator here is referencing this quote from his own 1835 book Modern Egyptians:
It is commonly affirmed, that malicious or disturbed genii very often station themselves on the roofs, or at the windows, of houses in Cairo, and other towns of Egypt, and throw bricks and stones down into the streets and courts. A few days ago, I was told of a case of this kind, which had alarmed the people in the main street of the metropolis for a whole week; many bricks having been thrown down from some of the houses every day during this period, but nobody killed or wounded. I went to the scene of these pretended pranks of the genii, to witness them, and to make inquiries on the subjects; but on my arrivals there, I was told that the “regm” (that is, the throwing) had ceased. I found no one who denied the throwing down of the bricks, or doubted that it was the work of genii; and the general remark, on mentioning the subject, was, “God preserve us from their evil doings!”
This source (which itself is quoting Majmoo’ Fataawa al-Shaykh Ibn Uthaymeen (v. 1, p. 287-288)) attests to this history as well:
Undoubtedly the jinn can have a harmful effect on humans, and they could even kill them. They may harm a person by throwing stones at him, or by trying to terrify him, and other things that are proven in the sunnah (prophetic teachings) or indicated by real events.
This website which aggregates paranormal activities in Arabic countries claims to report a news story describing djinn throwing stones in Morocco in 2010.
As an additional aside, there are also instances in which djinn have stones thrown at them (presumably as a dramatic reversal of roles). The open-access translation of One Thousand and One Nights linked above includes the observation that some Arabs have believed that shooting stars are stones thrown from heaven to kill evil djinn. This could potentially parallel the Stoning of the Devil (an allusion to the djinni Iblis) referenced in the original question. Also, one of the first stories in One Thousand and One Nights is "The Story of the Merchant and the Jinnee" which begins with a man throwing the pit of a date (called a stone) over his shoulder and accidentally killing a djinni's son.
Clearly, djinn are well-documented stone throwers. It seems apparent that the Magic card "Stone-throwing Devils" is referencing this. One might ask why "devils" is used instead of "djinn" since Magic the Gathering is no stranger to the word. I suspect that the designers were trying to reserve "djinn" (a rather uncommon word in English) for exceptional and rare creatures since only 4 "djinn" appear in Arabian Nights. The term "efreet" is also used a few times in the set - again in reference to rare creatures. With this goal in mind, using the word "devil" makes sense. "Devil" would also help to emphasize the obvious Biblical pun in the flavor text of the card.
Contextually translating "djinn" or "efreet" as "devil" or "demon" is not such a strange idea. This journal article argues in favor of using different English words to describe both the different levels of and different motivations of djinn. Both "devil" and "demon" are addressed specifically. This article admits that "djinn" has no direct English equivalent, so while transliterating the word might be acceptable, it doesn't seem beyond the pale to find a common English word that conveys the relevant meaning in context.
To summarize: "Stone-throwing devils" is not a slur as such, and historically, it has no immediate connection to Islam. However, when put into a modern Arabic context it can begin to carry some contextual baggage. In the specific context in which the phrase is used here (namely, an Arabia-inspired fantasy setting), it seems clear that that baggage has been misplaced.
EDIT: @TaliesinMerlin tracked down this article from 2002 in which the designer Richard Garfield explains the origin of this card's name:
"An interesting story," said Garfield of the origins of this card name. "One island was occupied by stone-throwing devils in one of the stories. But some people were upset with me for its use, because apparently 'stone-throwing devil' is a derogatory term for someone. I suspect that 'stone-throwing devil' has been an expression for a long time, and its meanings have changed or been applied to different people."
This would suggest that the controversy has existed for a rather long time already. Additionally, the description he provides is in-keeping with the stone-throwing djinn hypothesis proposed above. I have attempted to locate the story in question but have been unsuccessful. It is possibly a misremembered reference to Sinbad's Third Voyage in which giants kill Sinbad's crew by hurling stones at them.