How does a "chromogenic mixture" produce such pronounced color differences in this Agar Art?
She is referring to a mixture of chromogenic substrates: molecules which are more or less colourless until cleaved by a specific enzyme, releasing a coloured product.

For example X-gal is colourless until the enzyme beta-galactosidase hydrolyzes it, releasing a blue coloured product. If you spread a mixture of bacteria onto a plate, with some expressing beta-galactosidase and some not, you will see both blue and colourless colonies, as seen here:


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Chromogenic substrates are often used to create differential media that allow the differentiation of different species of bacteria. This plate, for example, contains several different chromogenic substrates (a mixture, if you will) for identifying the bacteria commonly found in urinary tract infections:



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If you wanted to make a picture with this plate, you could “paint” with Enterobacter spp. for blue, Staphylococcus aureus for yellow and S. saprophyticus for pink. Each species produces a specific enzyme that acts on a specific chromogenic substrate in the plate, changing its colour. 

Alternatively, you could express the desired enzymes recombinantly in one species.