What is "va'Te'azreni Chayil la'Milchamah"?
Malbim: In the first method, He girds him with strength, but it is not used for war (he does not fight). By contrast, in this method the strength is used for war.
Here it says "va'Te'azreni" with an Aleph. Why does it say in Shmuel II, 22:40 "va'Tazreni"?
Radak (Shmuel II, 22:40): Also there, it should say va'Te'azreni, like "va'Te'azreni Simchah" (30:12). For ease of pronunciation, the Aleph was omitted, and its Nekudah (Patach) was moved to the Tav.
Radak (Shmuel II, 22:40 citing his father): There it is Hifil, from the root Zere. You cast strength into all my limbs to make war.
Why did he say "Tachri'a Kamai Tachtai"?
Malbim: Even though in this method the strength is used for war, You lower those who rise against me "Tachtai", i.e. You do so in place of me.