Many read right over this without seeing what it says. The thousand that "at thy side" are your brothers, your compadres. the "ten thousand at your right hand" are different though. Think in terms of the time this was penned, when warriors went into battle armed with swords, which they used in THEIR RIGHT HANDS.
Yes, the "ten thousand at your right hand" are the enemy, killed with your sword.
Prasie God for His divine protection over our warriors.