Different imprint, same basic company.
Uhhhhhh... no, I don't think so.
Not a lawyer, nor an expert, but I think the situation is more complicated.
I believe Copyright law of the time had a definition for what qualified as 'published', so if you printed a book that you gave as a gift to friends and family that would not be considered published under Copyright law.
Motion Picture Funnies had copies printed so Lloyd Jaquet could show movie theater owners what the finished product would look like to sell them on the concept, but I don't think it would have qualified as published for Copyright law. Presumably if theater owners had bought the concept a full print run would have happened and Jaquet would have filed for Copyright.
So when Funnies Inc. became a comic book publisher he just sold some or all the material in the book to Martin Goodman who became the Copyright holder for those stories his company published.
Motion Picture Funnies was never put up for sale in the "wild" so is not technically a Golden Age comic book. Fandom didn't know this book existed until the 1970s when I think 8 copies were discovered among Loyd Jaquet's belongings.
It reminds me of a case where a 200 year old poem discovered & printed in the early 20th century got Copyright protection for the publisher since the poem had never been published before. Copyright law be crazy.