"Dulce Et Decorum Est" is not a sonnet. A sonnet is a particular type of poem which must demonstrate certain key features. Sonnets are fourteen lines long and adhere to a particular meter and rhyme scheme. Examples of sonnets would be Shakespeare's sonnet cycle. While the sonnet form has been widely used by many writers in different eras, and indeed by several poets of the First World War, it is not the form or structure Wilfred Owen is using here.
The structure and form of this poem do bear certain resemblances to a sonnet. Owen does use a rhyme scheme which runs ABABCDCD, and the first stanza has eight lines which mostly adhere to iambic pentameter, loosely speaking. One could argue that this is an octave, and that it, in conjunction with the following stanza, could be considered a sort of sonnet, as these two stanzas between them have fourteen lines. However, the poem continues on after this, and the first two stanzas do not culminate, as we might expect a sonnet to do, in a rhyming couplet. So, while it is possible that Owen had the meter and general sound of a sonnet in mind when he began writing, the sonnet form is one which is very rule-bound. While we sometimes find a double sonnet in poetry, where a poet has used two fourteen-line sets to convey an idea, that is not what Owen has done here.