Usually we're super-strict about keeping the speaker of a poem separate from the author of a poem. After all, poets often create fictional personas who they imagine to be speaking their work – not everything they write down is what they personally believe. But in the case of "Do Not Go Gentle into That Good Night," it's nearly impossible to separate the speaker of the poem, who is urging his father to struggle mightily with death, from the author Dylan Thomas, who was really upset about his own father's declining health and impending death. Maybe the best way to think of it is this: Thomas is using the speaker of his poem to say things to an imaginary father that might have been too difficult to say face-to-face to his own father, or that his father (who was dying at the time) wouldn't have had the energy to hear or understand. The speaker is Thomas's alter ego, composed of autobiographical elements, but still not quite the same as the man himself.
It's also interesting to notice that we don't know the speaker is using the first person until nearly the end of the poem, when he uses "me" and "I" in line 17. We have to shift our opinion of the speaker and his perspective once we're blindsided with the first-person stuff in the last stanza.