This actually makes a certain amount of sense for a violent insurgent group masquerading as a state. But all the reasons that this might make sense for ISIS underscore it'd be madness for the United States of America and other real countries to make money out of little pieces of metal.
The Islamic State is weak and unstable
ISIS currently controls a decent chunk of territory in Syria and western Iraq, and uses control over that territory to finance itself through oil smuggling and extortion. This is not so different from how any other resource-rich autocracy might operate its finances. But given its lack of international legitimacy, ISIS cannot stockpile foreign currency reserves or access the global banking system. ISIS is also at war with the governments of Syria and Iraq, is opposed by the main regional powers Saudi Arabia and Iran, and has antagonized the United States of America and its European allies.
Given that rather daunting list of foes, ISIS has done an excellent job of exploiting the deep divisions between their local opponents and not getting wiped out. But the odds that the Islamic State will cease to exist two or five or ten years from now are pretty high. Certainly much higher than the odds that the United States or Japan or France will be gone. Consequently, while scrip issued by the Islamic State would have some short-term utility if ISIS agents accepted it as payment, it would be useless as a store of value. Nobody would want to hold ISIS fiat money over the long-term, so it would be impossible to profitably operate a bank using ISIS money, or for ISIS money to serve as a useful medium of exchange.
The United States is a real country
Given ISIS' questionable prospects for long-term survival, fiat money is not a real option. The most practical thing for them to do in the short-term is probably to do exactly what a criminal enterprise would do and just rely on good old-fashioned US dollars. A number of countries with a history of state weakness, including El Salvador, do this and it works well enough. But given ISIS's long-term interest in establishing a Caliphate it might want to adopt the trappings of statehood. Stamping some kind of logo on pieces of metal and calling it currency fits the bill.
But it is a sign of strength that the United States of America (like Canada, and the UK, and Japan, etc.) doesn't resort to this kind of expedient. In economic terms, the gold standard is a bad idea. If you have a credible state infrastructure, then the logo itself does the work that you need. The American government not only has the ability to collect taxes payable in United States currency, but it will continue to do so for the foreseeable future. That makes pieces of paper marked legal tender (and bank accounts denominated in the same) both valuable and useful. ISIS's interest in gold coins is a sign of its weakness — of the fact that as scary as ISIS is, nobody has faith in its long-term durability — and its need to bolster its credibility with precious metals.