These are legal U.S. tender, minted in the U.S. Not common in the U.S. but still valid.
Pay attention to your other coins though. Ecuador does mint its own coins that match the American ones identically (1, 5, 10, 25 and 50 centavos) and also has some older 1 sucre coins that match these 1 dollar coins. Those would not be legal tender in the U.S., I'm pretty sure.
Ecuadorians are very touchy about the condition of their paper bills. I tried to pay for a Panama hat with some cash that included a slightly torn but fully in tact $10, and the shop owner refused. As such, more durable dollar coins, which were minted by the US but never really caught on, are quite popular.
There's a few countries that use US currency as the premium currency. Its very bizarre to be halfway around the world and see US dollars, but its a strong and reliable currency in countries where the local currency is too volitile to use.
I have a lot of those "gold" dollar coins. For a long time after they came out, I'd ask the cashiers at stores and banks to trade me paper dollars for whatever gold coins they had available. Many times I had to dig into my stash to get by, so it's not like I'm sitting on a massive horde of them or anything, but I have about a hundred of them.
They used to use the Sucre. When it crashed a lot of people lost a lot of money. I wish I knew more about that, and why they decided to bend over and use the world's biggest terrorist organization's currency.
Sure, when you hand the cashier some US dollar coins, nobody bats an eye, but when I hand the cashier a stack of Australian $1 notes, everybody loses their minds!