The Metamorphosis is existentialist because Gregor's choice to support to his family ultimately leads to negative consequences, and while a traditional manner of thinking would call Gregor's support of his family something he must do, it is actually something he chooses to do, therefore suffering from the outcome.
How is Gregor an existential failure?
Gregor, due to his family's financial issue and fear of being shame in the society, is unable to burst of his inner pressure. This pressure causes him to look for death as a suitable tool to escape of absurdity that society and his family offered him earlier.
What is Gregor's existential crisis?
Gregor's fatal flaw is that he tries to create a life by doing for others rather than by being himself. As a result, he dies alone without ever really knowing himself or giving others the opportunity to know him.