This morning I read this sentence (see story):
On July 24th and again on July 29th, Egyptian police did shoot dead unarmed African migrants attempting to cross that border.
Why "did shoot" and not "shot"?
The "did" is there to add emphasis. Similar to:
"You didn't read the book."
"Yes, I DID read the book."
If you look at the context where this appears in the article, "do" is being used to contrast that clause with what has come before. It's kind of like a focus marker, except that it also triggers a change in verbal morphology because "do" takes tense here instead of the main verb "shoot". Compare:
"I asked for cake."
"I DID ask for cake."
Here it's more obvious that the tense resides in the auxiliary and leaves the main verb without tense (hence it appears in the same form as the present).
This is an example of a English phenomenon know as do-support, whereby a dummy "do" is inserted to ensure that an utterance has tense. It is usually restricted to utterances where the movement of the verb is somehow blocked: e.g., in a negative statement or a question. It can also be used for emphasis as noted, but isn't grammatically required. I would venture to say that this isn't as natural or forthcoming in native conversation, and does a diservice to the comprehension here. For what it's worth, I very much prefer "shot dead".