question 1) Why is this definition so roundabout?
In my opinion, I don't think the definition is roundabout. The fact that the definition of energy seems roundabout has more to do with the fact that energy is continuously being transferred between objects or systems that are not isolated from one another (i.e., objects not having boundaries that prevent both work and heat transfer as well as mass transfer).
Energy can be considered to be a property that an object possesses. The object’s internal energy is the sum of its kinetic and potential energies at the molecular level, as reflected in properties of the object such as its temperature (for kinetic) and the intermolecular forces (for potential). This is generally the realm of thermodynamics.
The objects external energy is the sum of its kinetic and potential energies at macroscopic level, i.e. with respect to the mass as a whole, and is determined with respect to an external frame of reference. Examples are gravitational potential energy and the kinetic energy of the object as a whole due to its position or velocity, respectively, with respect to an external frame of reference. The external energy is generally in the realm of mechanics.
Work is one of two forms of energy transfer between objects. The other is heat. The former is generally in the realm of both mechanics and thermodynamics. The latter is generally in the realm of thermodynamics.
If an object possesses energy it has the capacity to do work. What this means is that it has the capacity of transferring some energy from itself to some other object by applying a force through a distance, resulting in a change in the energy (internal and/or external) of itself (decrease) and the other object (increase), based on conservation of energy.
question 2) How exactly does a force transfer energy?
I believe the examples given by Phillip Wood answer this. I will add another simple example in the context of my answer to question 1.
I am sitting still at my desk with my feet on the floor. Portions of my body possess external potential energy with respect to the floor depending on the product of their mass and their height with respect to the floor. Since I am sitting still, I have no external kinetic energy with respect to the frame of reference of the room I am in.
I have internal kinetic and potential energies (at the molecular level) as reflected by my body temperature and intermolecular forces. These internal energies are due to conversion of chemical energy by mean of metabolic processes. If I am sitting still there is no work transfer between me and other still objects in the room. Since my body temperature is greater than the room temperature, there is heat transfer from my body to the room.
I now decide to take an object from my desk and put it on a shelf above the desk. To do this I must apply a force to the object against the force of gravity to lift the object. That force times the increase in height of the object is energy transfer by work from me to the object. That work increases its gravitational potential energy at the expense of my internal energy. By virtue of my increasing the gravitational potential energy of the object that was on my desk, I have increased that objects capacity to do work, given the opportunity and circumstances to do so.
Hope this helps.