Paul selflessness in riding his rocking horse in a frenzy to determine the winners of the horse races is what drives him to death; moreover, it is, ironically, a selflessness that is unrecognized by his selfish mother who thinks only of her own imagined plight. Paul dies from love for his mother, but her heart is "a stone."
Yes, Paul’s death is ironic because his mother was completely selfish. He died because of her. He was tryingto help her so she could have all she needed. She was at a party while he was getting sicker and sicker. She was not able to see what he was doing for her sake. The sexual/Oedipus element is ironic too. The Oedipus complex suggests that a boy wants to possess his mother, and the rocking horse riding can be considered a sexual metaphor.