The sheet music is what it is. Modern instrumental notation beams on the major accents and subdivides note values with ties that run across a major accent. Modern vocal notation these days tends to do the same but beamed according to syllables in past centuries.
This does neither. It follows the syncopation but otherwise still beams per beat. We are talking about a song for young children: the typesetter likely felt that using ties in bean-counting style was more likely to damage than help the execution, either by confusing the singers or by resulting in extra stresses in the middle of notes, defeating syncopation. The other options of not beaming at all or at beaming across the whole measure apparently did not appeal to the typesetter, possibly because of introducing too much of a visual discrepancy to every second measure.
In the end, notation, like typography, is supposed to serve its audience. It does that by being helpful and unambiguous. The core audience here isn't a brass ensemble, but even a brass ensemble would have no problems figuring out what to play here in spite of being used to seeing it notated differently.
The main problem posing itself for notation like this is just at which point you do switch to more standard notation. Because the underlying principles of this notation are easy to keep consistent with this song. But as complexity grows, making decisions becomes harder.