offer and contract

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.