Roaming Throne's last ability doesn't copy the triggered ability; it just causes the ability to trigger an additional time. Any choices made as you put the ability onto the stack, such as modes and targets, are made separately for each instance of the ability. Any choices made on resolution, such as whether to put counters on a permanent, are also made individually.

If you control two Roaming Thrones with the same chosen creature type, triggered abilities of other creatures you control of the chosen type trigger three times. Three such Roaming Thrones result in four triggered abilities, and so on.