The type of enzyme inhibition in which xanthine oxidase is inhibited by allopurinol is an example of:
Suicide Inhibition:

Otherwise called mechanism based inactivation.
Special class of irreversible inhibition.
Inhibitors are relatively unreactive, until they bind with the active site of specific enzyme.
Once the inhibitor binds to the enzyme, by the action of the enzyme, it is converted to a potent inhibitor enzyme.

Examples of Suicide Inhibition:

Allopurinol inhibit Xanthine Oxidase. Allopurinol converted to alloxanthine which irreversibly inhibit the enzyme.

Reference-  Satyanarayana Pg-95
Noncompetitive
Uncompetitive
Allosteric
Suicidal