What is torque-ampere ratio at electric machines? How it is related with machine efficiency?
Torque / amperage ratio means how much torque produced from consuming a specific amount of current. The more torque produced from the same amount of current results in a better efficiency of the overall machine.
Machine efficiency can be calculated by the following form : 

$$ \gamma  = \frac{P_{output}}{P_{input}} $$

Input power is the electrical power consumed from the main grid. Main grid voltage is constant across most nations around the world so power is dependant upon the current consuming.

Output power is the mechanical power available to do some work. 

$$P_{mech}=T \omega$$

So more torque / amperage ratio means the reduction of the overall cost and the more available work to be done.