Never use Ni-MH batteries in a toy?
This model has a low quality metal-brushed 'toy' motor which has very limited lifespan. It doesn't appear to have a current limiter or overload cutout, and is probably controlled by a simple on/off switch. 

Alkaline cells have higher nominal voltage than NimH, but under heavy load a good NiMH will produce higher voltage for longer. In the graph below the performance of a Sanyo Eneloop (low self-disharge NiMH) and high capacity NiMH are compared to a typical Alkaline cell at 1A discharge. The alkaline can only manage about half an hour at an average voltage below 1.2V, whereas the high capacity NiMH gets over 2 hours mostly above 1.2V. The Eneloop is even more powerful, but has slightly shorter run time due to its smaller capacity.

     

The extended run time and higher voltage from NiMH would wear the motor out faster, and if stalled the battery could deliver enough current to burn out the motor and/or wiring. Apart from the potential fire risk, the result would be an unhappy customer who might blame the manufacturer for producing a poorly designed toy. 

By specifying Alkaline only, Tamiya avoids having to improve the electronics to work with better batteries. At the time that this model was designed (1987) good quality motors and sophisticated electronic devices were relatively expensive, so that may have been a wise decision.