In this study, we focus on characterising the complex network dynamics of in vitro neuronal system of live biological cells during two distinct activity states: spontaneous rest state and engagement in a real-time (closed-loop) game environment. We use DishBrain which is a system that embodies in vitro neural networks with in silico computation using a high-density multi-electrode array. First, we embed the spiking activity of these channels in a lower-dimensional space using various representation learning methods. We then extract a subset of representative channels that are consistent across all of the neuronal preparations. Next, by analyzing these low-dimensional representations, we explore the patterns of macroscopic neuronal network dynamics during the learning process. Remarkably, our findings indicate that just using the low-dimensional embedding of representative channels is sufficient to differentiate the neuronal culture during the Rest and Gameplay conditions. Furthermore, we characterise the evolving neuronal connectivity patterns within the Dish-Brain system over time during Gameplay in comparison to the Rest condition. Notably, our investigation shows dynamic changes in the overall connectivity within the same region and across multiple regions on the multi-electrode array only during Gameplay. These findings underscore the plasticity of these neuronal networks in response to external stimuli and highlight the potential for modulating connectivity in a controlled environment. The ability to distinguish between neuronal states using reduced-dimensional representations points to the presence of underlying patterns that could be pivotal for real-time monitoring and manipulation of neuronal cultures. Additionally, this provides insight into how biological based information processing systems rapidly adapt and learn and may lead to new or improved algorithms.