FPTP itself is not deliberately engineered to lead to two parties and I doubt that was the intent of the framers anyways. For a time at the beginning of U.S. government the whole notion of strong political parties was considered bad for governance anyways; people were supposed to represent their constituents or their state.

However nowadays the two major parties certainly do cooperate in ensuring that there remain only two major parties, rather aggressively going even further than FPTP would otherwise lead to in keeping additional political parties weak. It's easier to get elected without a party affiliation at all than to be elected as a party other than D or R.