Nomi The connection between gamification and NE would be how they both try to elicit some behavior or effect in someone. Gamification might want to get you "hooked" on something, and this seems pretty similar to NE rewiring your brain w.r.t something. They both try to induce some deep effects in the brain (at least in theory).
Moreover, NE could be just one way of how gamification can work on the neurological side.
An example would be a game app where you hunt for treasures. Gamification could be effectuated by numerous calls to action: "Tap on this shiny chest and get a reward", the chest being shiny and slowly swaying side to side. Now, if that chest was to sway in a carefully designed rhythmic manner, it might perhaps induce some sort of entrainment..
Going a bit more scientific ..
The way I see it is that Neural Entrainment is a potential mechanism that helps neuroplasticity. Neuroplasticity is the ability in our brain to adapt to new contexts and extrapolate solutions even when the context is new. This adaptation is memory-triggered, which means that when facing new environments, the brain tries to search for familiar clues. The more clues you can match with existing memories, the easier the adaptation. That being said, NE (as far as I understand it) is thought to help with this, especially when it comes to memory.
The functional role of neural oscillations is still not fully understood;^ however they have been shown to correlate with emotional responses, motor control, and a number of cognitive functions including information transfer, perception, and memory.^ Specifically, neural oscillations, in particular theta activity, are extensively linked to memory function, and coupling between theta and gamma activity is considered to be vital for memory functions, including episodic memory.
Now if we were to look at technology's effects on neuroplasticity, we would notice that there are many observed cases when the use of virtual tech is beneficial, as pointed out in this study and its references: https://www.frontiersin.org/articles/10.3389/fnhum.2014.00218/full
One thing you might notice in that study is that they mention a lot of "rewards" and "feedback" ideas, both of which are pillars of Gamification strategies. In short, they noticed that certain games that include "rewards" but also multi-tasking can help improve and sustain cognitive benefits (neuroplasticity). Importantly, they noticed that they need both the rewards and the multi-tasking elements to do so. So there is a clear indication that rewards are important in improving neuroplasticity.
So basically my intuition is:
- Neural Entrainment -> Enhanced Memory -> Neuroplasticity Improvement
- Rewards and Feedbacks (gamification) -> Enhanced Cognition and Memory -> Neuroplasticity Improvement