Warning anyone who might be accidentally mixed in with them ahead of time doesn’t entirely fit with the claim of extreme ruthlessness. The Amalekites seem to have been basically nomadic raiders - a tribe of brigands, killing and pillaging anyone who seemed vulnerable. Fighting the Amalekites thus has similar positive and negative aspects to a “war on terrorism” - on the one hand, there seems to be little practical option for protecting potential victims other than killing those who are dedicated to violence; on the other, there’s plenty of risk of non-target deaths, using such a slogan as an excuse for self-interest, etc.
Note also that to completely wipe out was standard military hyperbole. Egypt claimed to have wiped out Israel a bit before 1200 BC. Rahab and the Gibeonites show that joining Israel was an alternative to judgement; note also the further existence of Amalekites after Saul is described as wiping them all out (I Sam 30 [which adds the detail of Amalekites being cruel to their slaves]; 2 Sam 1:13).
An important difference between the commands to Israel to destroy particular enemies and much other religion-invoking warfare is that Israel was routinely warned that this did not reflect their own merit. Israel would face similar judgement if they were unfaithful; they were not earning merit by bringing judgement on others. This is quite different from a crusade or jihad.