The thing that surprised me is that it's C-only: there doesn't seem to be any ASM part in the sources. I guess the need for ASM came later.
In comparison, most Mac apps that have been open-sourced by the same museum (MacPaint, Photoshop,...) seem to include quite a large part of 68k assembly.
From what I learned by looking over the source code, the need to use assembly language was not acute because "Deluxe Paint" could harness the Blitter. It even hardly mattered that the 'C' compiler used in 1985/1986 was not an optimizing compiler. Most of the work done with "Deluxe Paint" is driven by user interaction, which is slow...
The Macintosh did not have a co-processor which would have helped the applications, hence the need to use (presumably hand-optimized) assembly language. Also, the Macintosh Pascal and 'C' compilers were just as poor at producing optimized code as the Lattice 'C' compiler used for "Deluxe Paint" at the time.
That said, the differences in these approaches even extends to the respective operating system. For example, the Amiga "graphics.library" is built around the co-processors (Denise, Agnus) and is written mostly in 'C' with significant portions rewritten or specifically written in assembly language. The original Macintosh QuickDraw by comparison was written entirely in assembly language, with no higher level language (Pascal) involved.