National Interest defines a rules-based international order as
The notion that all are bound by a global set of rules, an international law above power
The Council on Foreign Relations defines it similarly:
there exists a Western liberal international order whose distinctive values, norms, laws, and institutions were designed to inform and govern state conduct. This order originated in Europe but achieved full expression only with the U.S. rise to global leadership (or hegemony), as the post-1945 United States combined power and purpose to forge a multilateral world order, using a mixture of persuasion, incentives, and coercion to do so.
It may be worth noting that as described, this was a western system. It included the United States and Europe and excluded the Soviet Union and China.
What US Secretary of State Rex Tillerson seems to be saying is that he wants China to join the US/European system. Part of the problem may be that what China wants is a system that they get to help build. Another part of the problem is that with the demise of the Soviet Union, the west is less willing to accept states that are not democracies in the western sense. China, as one of those states, would prefer to be accepted as they are. They are unwilling to change.
This tends to produce a lot of talking past each other. Tillerson saying something. Then China uses the same words but means something else.
A specific problem here is that the US and Europe have come to the conclusion that loaning developing countries money for infrastructure projects hurts more than it helps. So they have mostly stopped doing that. Meanwhile, China continues.