They aren’t showing the reason he got the red card, they keep showing the “third” phase of the exchange.
The original replay from a distance showed there was an initial coming together (first phase), then the Sheffield player came back and kicked through the back of the Wrexham players legs (second phase), then the Wrexham player stopped and started shouting at the fourth official about the kick and the Sheffield player collided with him again (third phase), which is the bit they keep showing.
The kick out was intentional, forceful, and petulant, was definitely deserving of a red by the letter of the law.