Is there some sort of rule that says that there can only be two political parties.

No, but I think the issue lies with their system of government. As a presidential republic they don’t have parliamentary government where parties enter coalitions to form the executive, so smaller parties have no good way to get established and share executive power and responsibility while growing.

Couple that with the voting system which also favours the trend to only two parties, and there you have the mess.

PS: They have the Green Party and the Libertarian Party, but they remain at the fringe and largely irrelevant. No seats for either of them.