In general, parental involvement/engagement has lots of positive social, emotional, cognitive, and academic effects for a child's development. Some evidence suggests that the positive effects of relatively general factors like improved parent-child relationship, increasing motivation and (positive) expectations, etc., are stronger than the specific benefits of learning particular educational material. Based on this, I would say that if you and your daughter enjoy doing these learning to read activities, then they will have positive effects because they will teach your daughter that reading is important and that her parents care about her and her intellectual/academic development, whether or not your daughter specifically learns to read from this DVD.
On the specific subject of reading, it is important to keep in mind that the vast majority of children will learn to read regardless of the particular method of instruction. Phonics-based methods (which emphasize letter-sound correspondences) are generally thought to be more effective than whole-word methods, especially for children at risk for reading disability/dyslexia. However, even the most die-hard phonics supporters acknowledge that phonics needs to be embedded within a comprehensive reading instruction program that makes reading fun and meaningful. In other words, phonics is the best method, but any fun reading activities that you do at home to get her interested in books will have positive effects.
A few references:
Nokali, Bachman, & Votruba-Drzal (2010). Parent Involvement and Children's Academic and Social Development in Elementary School. Child Development, 81(3), 988–1005.
Senechal & LeFevre (2002). Parental Involvement in the Development of Children's Reading Skill: A Five-Year Longitudinal Study. Child Development, 73(2), 445-460.
Rayner, K., Foorman, B. R., Perfetti, C. A., Pesetsky, D., & Seidenberg, M. S. (2001). How Psychological Science Informs the Teaching of Reading. Psychological Science in the Public Interest Monograph, 2, 31-74.
Ehri, Nunes, Stahl, & Willows (2001). Systematic phonics instruction helps students learn to read: Evidence from the National Reading Panels meta-analysis. Review of Educational Research, 71, 393–447. [Note: there has been some statistically complex back-and-forth regarding this report, but I believe the original finding still stands.).