The sentence should be corrected as follows:
1) Replace "he" with "they": the noun "dolphins" is in the plural in the sentence so the personal pronoun that should be used is "they" as "he" is a singular pronoun (noun-pronoun agreement)
2) Replace "though" with "until": The subordinating conjunction "though" is used to connect contrasting ideas and does not reflect the meaning of the sentence. In this case, the correct word is "until" which is a subordinating conjuction of time.
The dolphins circled playfully around the ship until they swam somewhere else.