Are the nords of skyrim the only ones with battlecries such as skyrim is for the nords. Would the redguards or elves have their own?

Battlecry like the ability? or the Thu'um

The ability is a racial trait, The Altmer have Highborn, Orcs have Berserker Rage...... etc

I believe he means audible battle cries, not abilities, like what we here when we fight certain Nords or Stormcloaks in-game. To answer your question I suppose it would depend on the situation if and if it merits it.