1) There was an actual agreement between Guillory and Vogt that they would be a 50% owners. The YC application is a memorialization of the fact that this agreement existed.
2) Even if there wasn't an actual agreement, Cruise is using IP that Guillory developed.
The relevance of the YC application is this: Oral contracts are in general perfectly valid, unless they apply to a specific situation that requires a writing. A YC application listing the parties as 50-50 co-owners is at least strong evidence that an oral contract exists with those terms. It's reasonable to infer that if people have a writing proposing to do X, then they actually did X or have already agreed to do X.
While a vesting schedule might be typical, it's not going to be implied into existence unless there is some evidence the parties intended for there to be a vesting schedule. For similar reasons, questions of how much Guillory actually contributed will be relevant to (2) but not (1). A 50-50 joint venture is like marriage. Come the divorce, the assets will be split 50-50, even if one party earned all the money. The law won't come in and try to value peoples' contributions after the fact. That would be impractical. The law trusts that people say what they mean and mean what they say.
This case will turn on whether Vogt has any evidence to counteract the inference that may be made from the YC application. It will also turn on legal issues such as whether a writing, not just an oral contract, is required for the sort of arrangement Vogt and Guillory allegedly made, and if what's in the YC application is a sufficient writing to meet that requirement. IIRC stock issuance requires a signed writing in Delaware so that could be a stumbling block depending on how the agreement is framed.