The term “Standing” means for the ability of a party to demonstrate to the court sufficient connection to and harm from the law or action challenged to support that party’s participation in the case.
Trump should be able to demonstrate that his election and vote can be affected by a person who is not even eligible to run for President, since they are both running for the nomination.
There are no Constitutional limits on "running for President", the Constitution does not even recognize the electoral method of appointing electors, much less the process of "running for President".