Win $100 in art.
Compare "He paid me $1,000 but he paid me in one dollar notes!" or "She left in anger"
In = in the form/state of
OED:
19. Expressing physical, mental, or moral condition or state.
a. Followed by an abstract noun; e.g. in comfort, in doubt, in health, in hope, in pain, in sickness, in solitude, in sorrow, etc.
1928 N.Y. Times 4 May 24/3 It was just helping somebody in trouble.
Win $100 of art
Of = contextually associated with.
Win $100 of art = Win $100 associated contextually with art.
This is unclear in its meaning and is made worse by Art is uncountable in this context and therefore a concept rather than a physical quantity.
OED art (n.)
8a The expression or application of creative skill and imagination, typically in a visual form such as painting, drawing, or sculpture, producing works to be appreciated primarily for their beauty or emotional power.
To make sense you would need the plural, countable form "artworks" or "works of art".