I included the card in a deck for Koth and played it in legacy Battle Trials, still no triggers activated upon attack, besides Haste (which worked in both cases).
The abilities trigger based on how many more creatures the opponent has. It’s hard to tell from the screenshots provided, but in the second one it appears Greg only has one creature while you have two, so X = 0 and Warchief doesn’t get reinforced. The gem destruction is a “Then” clause, meaning it only triggers if the prior ability triggers. (And since X = 0, there are no gems to be destroyed anyway.)