It is important to be very clear about definitions when responding to this question. A domestic tragedy is a sub genre of tragedy that is distinguished from other forms of tragedy by the action involving middle or lower class individuals who are not important figures in society. The first domestic tragedies were actually written during the English Renaissance period, with critics agreeing that the first example of this form was entitled Arden of Faversham, first performed in 1592, which featured the murder of a middle class man by his wife who was unfaithful.
Based on this definition, it is very difficult to argue that Othello is actually a domestic tragedy. Othello is an important figure in Venetian society and he marries the daughter of an important dignitary. This play therefore appears to be much more of a classical tragedy in terms of corresponding to the guidelines for a tragedy as dictated by Aristotle, who argued that tragedies must concern important, aristocratic figures. The only way in which this could be questioned would be through analysing the figure of Othello as an outsider, who simultaneously belongs but also is restricted from belonging to Venetian society. This is something that Othello himself draws attention to in his final speech:
Then must you speak
Of one that loved not wisely but too well,
Of one not easily jealous but, being wrought,
Perplexed in the extreme; of one whose hand,
Like the base Indian, threw a pearl away
Richer than all his tribe; of one whose subdued eyes,
Albeit unused to the melting mood,
Drop tears as fast as the Arabian trees
Their medicinable gum. Set you down this,
And say besides that in Aleppo once,
Where a malignant and a turbaned Turk
Beat a Venetian and traduced the state,
I took by th’ throat the circumcised dog
And smote him thus.
Othello, just before killing himself, speaks with such eloquence and reminds the audience of his prowess in battle, but at the same time identifies himself with the "turbaned Turk," also identifying himself as an outsider and a potential enemy of the state. Othello is therefore not the normal figure for a classical tragedy, as he is not an aristocratic member of society; however, it is clear that he is not middle or working class and his death does impact Venetian society of which he is a part, however tenuous that claim of belonging is. In conclusion, this makes it very difficult to support the view that this play is a domestic tragedy.