Unlike quasi-static robotic manipulation tasks like pick-and-place, dynamic tasks such as non-prehensile manipulation pose greater challenges, especially for vision-based control. Successful control requires the extraction of features relevant to the target task. In visual imitation learning settings, these features can be learnt by backpropagating the policy loss through the vision backbone. Yet, this approach tends to learn task-specific features with limited generalizability. Alternatively, learning world models can realize more generalizable vision backbones. Utilizing the learnt features, task-specific policies are subsequently trained. Commonly, these models are trained solely to predict the next RGB state from the current state and action taken. But only-RGB prediction might not fully-capture the task-relevant dynamics. In this work, we hypothesize that direct supervision of target dynamic states (Dynamics Mapping) can learn better dynamics-informed world models. Beside the next RGB reconstruction, the world model is also trained to directly predict position, velocity, and acceleration of environment rigid bodies. To verify our hypothesis, we designed a non-prehensile 2D environment tailored to two tasks: "Balance-Reaching" and "Bin-Dropping". When trained on the first task, dynamics mapping enhanced the task performance under different training configurations (Decoupled, Joint, End-to-End) and policy architectures (Feedforward, Recurrent). Notably, its most significant impact was for world model pretraining boosting the success rate from 21% to 85%. Although frozen dynamics-informed world models could generalize well to a task with in-domain dynamics, but poorly to a one with out-of-domain dynamics.