Not that the presumptions will turn out to be right, but just based on the presumptions:
The presumption is that the BOJ’s action will weaken the currency, stocks are up due to the weaker yen, which is presumed to support exports and restrain imports, and help with earnings translations
So the presumed increase in exports/higher stocks is not about total global sales/profits increasing. The presumed increase in exports is just about Japan gaining market share.
Which means the same presumptions lead to the further presumption that the equity gains in Japan from increased exports are at the expense of the ‘rest of world’s’ sales/profits/equity valuations/etc.
In other words, the equity rally in Japan is not based on the presumption that Japan will be an ‘engine of growth’ for the rest of world. Quite the opposite, in fact.