In this case, I'd argue that it means "begin something." Yes, missiles are something that are literally launched. But technically they're launching a strike, not a missile, if you analyze the sentence. You will also see "launch a strike" to talk about any kind of military operation, even ones that don't involve missiles.
What is the reason "to talk" is used there instead of "talk" even though "put" is used instead of "to put" in "I saw you put the key in your pocket".
These are different uses of the infinitive. Some uses require the marker "to".
The use "see '...' to talk about ..." uses an infinitive clause to give the purpose. You could rephrase this with "in order to talk about" or "with the purpose of talking about..." This is very general use of an infinitive and can be used with most verbs.
The second has a "verb of perception" and this type of verb can have a bare infinitive to indicate what was perceived. You could not replace "put" with "in order to put" because the infinitive clause here does not give the purpose. This type of infinitive is allowed because "see" is a verb of perception.
If you didn't put "to" in the first sentence then you would understand that you saw a list of words talking - and that is impossible.
