On the contrary, these games while seeming to help children learn, are on a problematic medium for them to digest them on. Hand-eye co-ordination is better learnt outside, and with three dimensional games, and eye muscles are still developing and gaining strength.
Some useful excerpts include:
Stimulation to a developing brain caused by overexposure to technologies (cell phones, internet, iPads, TV), has been shown to be associated with executive functioning and attention deficit, cognitive delays, impaired learning, increased impulsivity and decreased ability to self-regulate, e.g. tantrums (Small 2008, Pagini 2010).
Use of technology under the age of 12 years is detrimental to child development and learning (Rowan 2010).
Technology overuse is implicated as a causal factor in rising rates of child depression, anxiety, attachment disorder, attention deficit, autism, bipolar disorder, psychosis and problematic child behavior (Bristol University 2010, Mentzoni 2011, Shin 2011, Liberatore 2011, Robinson 2008).
High speed media content can contribute to attention deficit, as well as decreased concentration and memory, due to the brain pruning neuronal tracks to the frontal cortex (Christakis 2004, Small 2008)
is a decent if somewhat hyperbolic article (there are many, many others that more accurately address the points made). most of the points apply to TV instead of learning games, but learning games for toddlers have no empirical evidence base, so I'd treat them as equally suspect.
http://www.medicalnewstoday.com/articles/236211.php covers the current guidelines by the American Association of Pediatricians.
The report concludes that:
Although many video programs aimed at babies and toddlers are marketed as "educational" there is no evidence that they are.
Programs are only educational if children understand the content and context of what is being screened: studies have shown consistently that only the over-2s have this understanding.
Unstructured play is more valuable for the young developing brain than watching electronic media.
Unstructured play gives young children the opportunity to think creatively, learn how to problem solve, develop reasoning and develop motor skills.
Free play also helps them learn how to entertain themselves.
Young children need to interact with humans, not screens, and they learn best this way.
Watching TV and videos with your child may increase their understanding, but he or she will learn more from a live presentation.
Watching your own program when your young child is with you is "background media" for them and it detracts from the interaction between you: it may also interfere with their learning.
Watching TV and videos at bedtime is not a good sleep habit: it disrupts healthy sleep which can affect mood, behavior and learning.
Research shows that young children who watch a lot of TV and other media have a higher risk of delayed language development when they start school, although the reasons for this are unclear.
Your child has plenty of time to learn how to use technology, but it isn't necessary to start them on iPads and Android Tablets at three years of age. While
A host of research studies have shown that when media content are designed with research-based knowledge of how children use and understand media, and when they are designed to incorporate systematic academic or social curricula, children benefit (Schmidt, M. E., & Anderson, D. R. (2007); Fisch, S. M. (2004)). (David Kleeman, Huffington Post)
you could better enable them to learn the type of thing you seem to want to teach by using a Wii or similar. Limiting screen time to a maximum of 1-2 hours per day for under 8's seems to be the prevailing wisdom.
So to directly answer your question: no studies that I'm aware of show any benefits, however Google Scholar and other journal searching resources may be able to find a one. However, you should consider why you want to use a screen as a teaching aid and whether it provides any tangible benefits for your child - mostly it is implied by journal articles that parents providing screen time for children is ultimately for reasons to do with the parent rather than the child.