What vitamins exist for other animals but not humans?
The best example I can think of is taurine, which is a non-proteinogenic amino acid.

Taurine is "conditionally essential" for humans1, but essential for cats2,3.

References:

1: Stapleton, P. P., Charles, R. P., Redmond, H. P., &amp; Bouchier-Hayes, D. J. (1997). Taurine and human nutrition. Clinical nutrition, 16(3), 103-108.

2: Knopf, K., Sturman, J. A., Armstrong, M., &amp; Hayes, K. C. (1978). Taurine: an essential nutrient for the cat. The Journal of nutrition, 108(5), 773-778.

3: Markwell, P. J., &amp; Earle, K. E. (1995). Taurine: an essential nutrient for the cat. A brief review of the biochemistry of its requirement and the clinical consequences of deficiency. Nutrition research, 15(1), 53-58.