Why is the amount of DNA in plants so much lower than in animal tissue? Is this because plant cells are larger? (some plants like wheat have very large genomes, I wonder how that affects it too)

They are quoting the DNA concentration in g per kg of dry matter.

Plant cells have cell walls of cellulose, hemicellulose and pectin, which adds some dry weight that is absent in animals.

In addition, these seeds and tubers etc. we eat tend to be energy storage organs with a whole bunch of starch vs. not very much regular cell mass. It would be the same way if you ground up bone tissue and measured the DNA concentration.