The word "miracle" comes from a Latin word which might be translated more directly as "wonder". It's a thing which causes you to be amazed. In this broader sense, yes, both the atheist and the centurion can be said to have experienced something miraculous.
There are four words in the Greek of the New Testament that give a more Christian nuance to the idea of a miracle; these are dynameis (Strong's G1411: mighty powers, or works of great power), terasin (Strong's G5059: wonders, things which cause you to take notice), semeia (Strong's G4592: signs/symbols, something that helps you know what something is), and erga (Strong's G2041: actions, things that someone does). Let's handle these in reverse order.
Acts of God
When the New Testament talks about "acts of God" (erga tou theou), it is usually about normal people acting in a way that is godly and expresses His will. In this sense the centurion was certainly performing an act of God when he laid down his authority in faith before Jesus to beg a healing. It is not 100% clear whether explicit faith of this sort is necessary: Christian denominations are in my experience divided on whether people from other religions are capable of unintentionally doing the will of God due to acting justly, fairly, moderately, or kindly. (These things are talked about for example in the model of Christianity given us in Titus 2-3 as well as in many other instances.)
However we are more unified by scripture in one particular way which somewhat overrides this, also discussed in Titus briefly but expanded in much greater depth in Romans 3: that such good works are insufficient. So even if these are acts of faith, they do not give us the justification before God of having a clean soul -- whatever your denomination views that goal as being.
So this idea that we have in our modern language that something was an "act of God" is not really called that in the Bible. Instead the "acts of God" are really "Godly works": things that we do as a part of our new relationship with God.
In the legal vernacular an "act of God" is just one of those things which no human has causal responsibility for, like if your house gets hit by a bolt of lightning. Probably neither of these are "acts of God" in this sense: the 10-car pileup was probably caused by someone's recklessness and the servant was probably paralyzed due to some sort of physical trauma or accident which ultimately come down to someone's responsibility or another -- but perhaps it could have instead been a congenital defect or something, who knows.
Signs and Wonders
Here we get something far more meaty. Jesus's act is performed to indicate that He is a Prophet. His acts of healing are part of showing people that he is who he claims to be. These structure, for example, the gospel of John.
However I must here confess certain limitations of my own understanding. There are certain scriptures that are against the existence of signs; for example Jesus rebukes the Pharisees twice in Matthew by saying, "An evil and adulterous generation seeks for a sign, but no sign will be given to it except the sign of the prophet Jonah." The first time he explicates that it will simply be his death and resurrection. This is after these people have presumably seen Jesus perform miracles in Matt 12. We see some similar dissent in 1 Cor 22:24 that Jews are demanding signs and providing such signs is not the Christian approach. Furthermore, signs are not a 100% proof, though they are often used that way; see for example Matt 24:24 which says that false prophets will be doing great signs and wonders to lead people astray from the truth; but 2 Cor 12:12 has Paul saying 'The signs of a true apostle were performed among you with utmost patience, with signs and wonders and mighty works,' which I think is him insisting "I have been extremely generous with you!" but also seems to indicate that the "signs and wonders and mighty works" should make them realize that he is a "true apostle."
So I don't know exactly how to interpret all of this. In any case, it is straightforward to define a "signs miracle" as something which points to the power and authority of Jesus, as when someone heals in the name of Jesus or when Jesus heals the afflicted. The 10-car pileup obviously isn't a miracle in this sense. However, since false prophets will do signs, I am not sure it is an explicit requirement that one have faith to do them.
Jesus's act also inspires awe in us, startling us, shocking us out of our everyday world. Skipping around the Bible to see how this word is used, we find frightful situations "the sun shall be turned to darkness and the moon to blood," what appears to be an earthquake in Acts 4:31, and such. So those are wonders. I really think that these both need to be lumped together: these things are signs because they are wondrous.
And I think that awe is in many ways the kernel of faith. We hear of the faithful in the Old Testament described as people who "fear God". In Shinto, for example, anything that instills a great awe is called a kami, their notion of a (possibly-needing-veneration) spirit; in Indian religions they speak of "darśana", a spiritual sort of vision (awe?) that attends the actual beholding of something of power. So if awe is the kernel of all of these different faiths, then saying that something is a "wonder" is expressing some sort of faith -- it's just a question of where it's directed, whether productive (from our Christian perspective, at God) or unproductive (at self, false idols, evil).
Works of Great Power
That brings us to this last notion, but it's the most important one. 1 Cor 12:6, "there are varieties of activities, but it is the same God who empowers them all in everyone," literally could be saying "energizes" (erga comes from the singular ergon, which ultimately is where we get our word "energy"; the word "empowers" here is translated from "energematon" inward-energy-imbuing. It's not Christians who heal others, say, but Christ who heals others through our laying on hands. The power comes from Jesus directly; we are just proxies who have been empowered by Him. The things that we do, if they show power beyond what we ourselves have to offer, become these expressions of God's great power. Some of these are things that we are patiently awaiting in an age to come (Hebrews 6:5 uses dynameis this way); some are authority in the present over demons and illness (Luke 9:1); some are simply the power in the gift of God that we might be saved by our belief (Romans 1:16).
There are lots of expressions of God's raw power and how it can fill us, and the place it has carved for us to inherit (Ephesians 1).
I do not think that this is very strongly expressed by the chance survival of the atheist, but it might be. That same Ephesians 1 says, "In him we have obtained an inheritance, having been predestined according to the purpose of him who works all things according to the counsel of his will." Who am I to say that He didn't save the atheist, and might have even had a plan for him?