This whole episode doesn't make sense to me. Earth spotted Mars' stealth ballistic platforms, knocked down 4 of them, but a 5th launched a missile at Earth before it got destroyed. Earth let the lone missile burn all its way towards itself while doing nothing, and then only started shooting down the MIRVed warheads after they are deployed, missed 1 out of 20, and South America got nuked big time.
If Earth can intercept individual MIRVed warheads, why not do it earlier when it is still one big missile? And why not do it even further out by sending one or dozens of its own missile and intercept the Mars missile Patriot-vs-Scud style? The Mars missile is clearly hostile, accelerating towards Earth fast. Earth has a right to defend itself, so even if Earth shootshoots then Mars can not do anything (or can after losing everything else) about it.
With the above reasoning, does this whole first-strike capability even make sense when you are dealing with Earth (or Mars)? Earth can easily deployeddeploy thousands of missiles around LEO in the way it deployed its Planetary Defense Railgun.
A possible reasoning supporting the scenario depicted in the episode is that the lone missile shuts down its engine on most of its way towards Earth and is stealthy. If you try to enter the atmosphere the way the episode showed the warheads would burn up like meteors. But if interpreted this way the terminal velocity of the little warheads is actually pretty low and even easier to intercept.