Should we shoot running deer? In the middle 20th century running shots were standard. My first two whitetails...

Should we shoot running deer? In the middle 20th century running shots were standard. My first two whitetails were running flat out. I try to shoot them when they are standing, but sometimes they offer a running shot that just feels right. Took this 148-class in 1985 as it raced south to north at 125 yards with a 30-06, M70 Featherweight, 165-gran Nosler BT handload and 2-8X36 Leupold VX-III scope. One shot fired, one buck down. Was that unethical?  
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