He has more or less the same powers as Tzeentch; he's omniscient and can alter destinies to create a new destiny (so nothing is safe unless he doesn't fuck with it) with little more than a thought (that's right, he can fuck up your life just by thinking about it, and since you are here reading this, he probably has). So yes, he's another Mary Sue of Chaos that always wins regardless because he already won unless he loses, which would only be because he wanted to. At the furthest depths of functional insanity, the afflicted become attuned to the mind of Amon 'Chakai. They scream warnings that HE COMES, while the more stable Wizards/Psykers of the settings watch him carefully waiting for his eventual move. Which would probably end all resistance.
He also has an army made up of the Daemons of all factions, because he's manipulated everyone to serve his whims. Yeah...
Amon 'Chakai was most likely dropped in later editions because he makes Tzeentch irrelevant, because "I did it 30k ago" only really works for one individual on the same side without causing an echo. GW could've kept him in the game just filling the same role as Kairos Fateweaver with a different name, but GW isn't that clever.