If you ignore the breaks between stanzas, the rhyme scheme of the poem is ABAB repeated seven times. The third stanza rhymes with the last two lines of the second stanza. This part of the poem (from the last two lines of the second stanza to the first four lines of the fourth stanza) goes:
Dim through the misty panes and thick green light,
As under a green sea, I saw him drowning.
In all my dreams before my helpless sight,
He plunges at me, guttering, choking, drowning.
If in some smothering dreams, you too could pace
Behind the wagon that we flung him in,
And watch the white eyes writhing in his face,
His hanging face, like a devil’s sick of sin;
You can see that the ABAB rhyme scheme continues through the line breaks.
I suspect that the resemblance of the third and fourth stanzas to an upside down English sonnet is pure coincidence. Traditional English sonnets rhyme the last two lines, and if Wilfred Owen had wanted to make it clear that he included an upside down sonnet in his poem, he could have rhymed the two lines in the third stanza.
Owen does rhyme drowning with drowning here, defying the convention of English poetry that you should never rhyme a word with itself, and possibly making it harder for readers to realize that the third stanza rhymes with anything. This identical rhyme serves to emphasize the word drowning.