How can I tell which parts of this example drug are necessary parts of its pharmacophore?
From this? You can't. You need more information. Examples:


Do you know other drugs of this family? Which chemical features do they have in common? The interactions mediated by these features are likely important then.
Do you know how the drug is supposed to function (you mention competitive inhibition)? What does the natural substrate look like, and what are the similarities and dissimilarities to your example drug?


If you know only the figure shown above, you're really asked to identify electronic and steric features of the drug, that can possibly interact with the amino acid residues in the active site shown. In this case, all amino acid residues are capable of favourable interaction with a part of the example drug, so I would mention which interactions are present.

There are many good ionic interactions/H-bond interactions, which are qualitatively the strongest. 

One possibility is that it is sterically unfavourable to jam something into the hydrophobic pocket, but the payoff is, that this is what stabilises a certain (active or inactive) conformation of the protein, and the ionic/H-bond interactions simply serve to increase binding affinity / to keep the drug in place.

Another possibility is that the interaction with the hydrophobic pocket only increases binding affinity. The drug then might share the same ionic interactions as the real substrate, but placed differently in space, so they don't induce the same conformation change as the natural substrate.

The point is, without knowing what the action of the drug is, and some knowledge about other drugs of the same family or the natural ligand/substrate, anything beyond a listing of the interactions you can spot between the amino acid residues shown, and the chemical features of the drug will really just be guess work :-).