Regardless of the procedure in place, it does appear slighly bizarre that shoving someone with enough force to bowl them over is picked up by a guy who is ultimatley in place to ensure correct decisions are made yet no yellow card is forthcoming
Take it to the n th degree and that player later is guilty of simulation which is correctly assessed by var. He surely should be dismissed for his second yellow but wont be.
As a prev poster says, it gives off the impression its ok to do it and it makes it very awkward to caution a grass roots player for it this weekend.
With or without VAR, imo, a yellow card for adopting an aggressive attitude was required. You simply cannot, or should not, be permitted to walk up to a player and push them over and not recieve a card.