What does it mean to "write an image and GIF into the DNA of bacteria"?
The image was not in the DNA as such, only as an abstract representation that could be converted into an image from knowledge of the code.  Briefly, they encoded the image into DNA, using a couple of different strategies in which DNA represented pixels -- either with a single DNA base representing a pixel, or with a triplet representing a pixel.  Knowing the code they used, they could then extract the information and turn it back into an image.  

Quoting from the original article, CRISPR–Cas encoding of a digital movie into the genomes of a population of living bacteria:


  We began with an image and stored pixel values in a nucleotide code ... We first encoded images of a human hand using two different pixel-value-encoding strategies: a rigid strategy, in which 4 pixel colours were each specified by a different base; and a flexible strategy, in which 21 possible pixel colours were specified by a degenerate nucleotide triplet table ...  To distribute the information across multiple protospacers, we gave each protospacer a barcode that defined which pixel set (denoted as ‘pixet’) was encoded by the nucleotides in that spacer. Four nucleotides define each pixet, and the pixels of a given pixet are distributed across the image ... 


Their 21-color strategy is outlined in this figure:

 

Note: The paper isn't open-access. If you want a full-access version, Church often puts freely accessible versions of his papers on his web site; this paper, #441 on his list, is still shown as "in press" there, but check back at intervals and maybe it will be available there