Differing ways of saving the project buddy.
Option 1 - Folder (which contains all audio samples/files and any midi data say for ultrabeat drum machine/sampler or any of logics say pianos for example, within the folder would be the midi data for any of these tracks. I do not see it on your original post, midi data I mean.
Option 2 - logic project file, pretty much the same concept but logic will open the entirety of the production with all midi data again say for the entire drum sequence for the track made with ultrabeat, or again to use the built in sample library as an example, the project file method would also contain all midi data for the melodies or chord sequence of the piano.
Also any plugins (assuming all built in default logic plugiins would and should be there)
The plugins would still be there and so would the midi data for both methods of saving a logic session.
All I’m saying is you don’t mention this on your original post.
All I see is
“ I only have the data (Audio Files, Impulse Responses, Movie Files, Sampler Instruments, Samples, The Numbers Game.logic, Ultrabeat Samples folders) from this path: \Library\Application Support\Logic\Logic Studio Demo Songs\The Numbers Game”
So it’s a guessing game until I get near the computer and download it bud.