A monster bet by a Hong Kong-based hedge-fund manager is paying off with the “Pokémon Go” sensation.

Seth Fischer’s Oasis Management Co. stands to make tens of millions of dollars after a three-year campaign to push Nintendo Co. into mobile gaming. The success of “Pokémon Go,” a new smartphone game part-owned by Nintendo, has boosted the Japanese company’s shares by more than 50% in the past week, adding over $10 billion to its market capitalization.

Mr. Fischer, who had about 4% of his $1 billion fund in Nintendo at the end of June, is one of a growing cadre of foreign activist investors making money by pushing Japan’s sleepy corporate sector to be more shareholder-friendly.

U.S.-style activist campaigns like Mr. Fischer’s, which include critical letters, public presentations of alternative strategies and private prodding of management teams, are still uncommon in Japan, where news that a company is creating an investor-relations department has been known to send its stock soaring.

However, under Prime Minister Shinzo Abe, Japan’s government has recently encouraged companies to become more responsive to shareholders.