No, since psychic spells aren't prone to arcane spell failure
As identified in your linked question, psychic spellcasting doesn't suffer the arcane spell failure chance - because a psychic spell is not an arcane spell. A Mindblade magus casts their spells as psychic spells, not arcane ones, so such spells would never be subject to arcane spell failure. Further supporting this, psychic spells never have somatic components anyway:
Therefore, psychic spells never have verbal or somatic components, and have only expensive material components.
And arcane spell failure chance, even if it weren't specifically scoped to arcane spells, only affects spells with a somatic component:
If the spell lacks a somatic component, however, it can be cast with no chance of arcane spell failure.
So there's no way a psychic spell could be affected by arcane spell failure.
The Mindblade archetype doesn't alter or replace the basic proficiencies granted by the magus class, so it does still include the mention that the caster ignores arcane spell failure chance due to light armour for magus spells. As written, though, that particular feature is redundant for the Mindblade, and can be ignored.
It might be that it passes unmentioned due to an oversight in the Mindblade's description - or simply for brevity, since it makes no functional change to the Mindblade's abilities and you can save some wordcount by leaving it unchanged. Either way, you shouldn't read anything into the fact that it's unchanged by the archtype - a Mindblade shouldn't have to worry about arcane spell failure.