Yes, the play presented by Peter Quince and his actors, aka the mechanical, is a tragedy.  They do not intend to present it as a comedy but because they are not trained professionals, they don't know they are being funny.  They are trying to present it seriously.  The comments from the audience don't help, in fact, they are distracting and at time extremely rude which reveals some things about the men (Theseus, Lysander, and Demetrius).  The local workman are trying their hardest to do their play justice.  Their intention is serious and if played properly, the actors don't play it for laughs.  To be most effective, the actors must play it straight since the characters aren't trying to be funny.

The reason it is turned on its head is that their performance ends up mocking the recently married lovers.