The payment of hush money would have counted as a campaign contribution regardless of the source. If he paid it personally it would have been reportable. If Cohen paid it it would have been reportable. If a third party paid it it would have been reportable.
The reason it would have been reportable is because it provided benefit to the campaign. Covering up negative news is a benefit to the campaign, so if he paid it himself it would still have been a campaign contribution he would have to report.
By covering up the payment he is taking or making a campaign contribution in violation of FEC rules. By suppressing the story of his affair with Stormy Daniels he is contributing to his campaign and failure to disclose makes this a crime.
The fact that he committed a crime by failing to report a campaign contribution is what makes the payment itself part of a felony rather than a misdemeanor. In New York law they do not have to prove the specific electoral crime itself for this set of falsifications of business records to be related to a felony level crime and therefore felonious. The jury instructions approved by the judge specifically say that the jurors can find that he violated one of several options of law for raising this to a felony.