In the Dwarf traits says:
In PHB (p.222)says for the heavy load: 'Carrying such a load requires both hands'. Does it means that the dwarf cannot attack while encumbered? So the Dwarf can just move with no penalty?
the dwarf can still kick people, or use his load as an improvised weapon (if the DM allows), and because opf his encumbered speed can move without penalty.
Still, if you're in combat it is pretty useless. Or will you start throwing staff off you. On the other hand, the dwarf's not pull me, not push me feature is great.
It's still reasonably impressive to be able to move at normal speed when another race would be slowed, even if that means you have to dump your pack if you end up in combat.
The dwarven cleric in my current campaign has used this twice to grab fallen comrades and drag them out of the line of fire. Something none of the other characters would have been able to do without getting swarmed.