There is offer, (counter-offer, counter-counter-offer...), acceptance and then contract.
Escalation clause belongs in the offer, not in contract.
A valid contract cannot have essential terms (price, quantity/location) missing. So I assume your valid contract has those terms in definite essential terms.
"我的问题就是，如果他们没有及时提出竞争者的合同要我match, 我是否有权力要求他们履行不需要match的合同。 "
This is the wrong question. It doesn't matter whether they gave you a competing offer or not. The question is WHEN did they show you the competing offer. Before the contract formation, or after contract formation.
Please talk to a lawyer. I am tired of playing your puzzle.
