AFAIK, this can't be done in any reasonable way with Bitcoin Core and its derivatives.
The only way I know to do it with Bitcoin Core is to use
importmulti to add your address(es) to the wallet as watch-only, but this requires a full blockchain rescan in order to compute the balance. This takes several minutes to hours depending on the speed of your hardware.
(Note that the bitcoin.it link you gave is obsolete and only covers the API up to version 0.8, so you won't find these commands listed there.)
You'd need to use some other software that actually indexes all transactions in the blockchain by their receiving addresses. This is what a block explorer does, for instance.
We have had a lot of other questions similar to this, so maybe there are some suggestions there: https://bitcoin.stackexchange.com/search?q=get+address+balance