Intrinsic value, in reference to money, is the value is has when the moneyness, or the exchange value, is removed.
For bitcoins, that is nothing. For fiat money, it is the paper value, you can decorate your walls or wipe your ass with it. Zimbabwean dollars has so little money value for the time being, its intrinsic value is dominant.
For gold, it is the technical use in electronics, it can be used to print title on bibles, it can be used to cover other metals for prettyness. For gold rings etc, the beauty is the value. Maybe for really heavy arm rings and the like, the owner also considers the money value of the ring to be useful sometimes in the future.
If you use the wider definition of intrinsic, as essential, natural, or from deep inside, then you are correct, nothing has intrinsic economic value, only use value as expressed by each actor on the market.
The special thing with money, is that when a commodity starts being used as the preferred commodity, it gains more value than its use value. for instance, if gold should again become useful as money, its value would rise, while silver and other commodities would stay put. Same if silver should become new money, it might go higher than gold in value.
This additional value is the exchange value, or the value of its moneyness. You could say that it is the use value of its service of facilitating indirect exchanges on the market.
At the time of the gold standard, a fully backed note (a note saying it represents some mass of gold) was worth more than the same mass of gold, even if the note holder had to pay the bank to store the gold safely. That was because the note was more handy in making exhanges.
So different money types has two value components, its exchange value and its intrinsic value.