Why is activation energy drawn in a potential energy diagram in reactions?
The activation energy is not the average kinetic energy that the colliding particles need in order to successfully react. Instead, it is the energy barrier between reactants and products. Often, the energy required to cross the barrier comes from the kinetic energy of collisions.

To describe the rate of a reaction there are two models, the Arrhenius model and the more sophisticate Eyring model:

The Arrhenius model uses the activation energy, defined as the energy required to reach the transition state; the "energy" here is of various nature, not only kinetic an includes the chemical potential. 

The Eyring model uses the Gibbs energy of activation for the transition state that includes an enthalpy and an entropy term ($ΔG^‡= ΔH^‡ – T ΔS^‡$). In comparison, for a unimolecular, one-step reaction, the activation energy can be approximately expressed as $E_a = ΔH^‡ + RT$.

There are different y-axis in these diagrams as explained in a related answer:
Y-axis of the reaction co-ordinate graph. Depending on the model and reaction you want to study you can use the Gibbs energy (Eyring model), energy in general (Arrhenius model) or enthalpy in case you want to show the heat absorbed or released in a reaction at constant pressure.

Why does your graph show potential energy?

In simple terms, potential energy is stored energy while kinetic energy is the energy of motion. Potential energy is converted into kinetic energy, therefore you can account for the latter including it in the overall potential energy.