You can use GROUP_CONCAT:

SELECT person_id, GROUP_CONCAT(hobbies SEPARATOR ', ')
FROM peoples_hobbies
GROUP BY person_id;

As Ludwig stated in his comment, you can add the DISTINCT operator to avoid duplicates:

SELECT person_id, GROUP_CONCAT(DISTINCT hobbies SEPARATOR ', ')
FROM peoples_hobbies 
GROUP BY person_id;

As Jan stated in their comment, you can also sort the values before imploding it using ORDER BY:

SELECT person_id, GROUP_CONCAT(hobbies ORDER BY hobbies ASC SEPARATOR ', ')
FROM peoples_hobbies
GROUP BY person_id;

As Dag stated in his comment, there is a 1024 byte limit on the result. To solve this, run this query before your query:

SET group_concat_max_len = 2048;

Of course, you can change 2048 according to your needs. To calculate and assign the value:

SET group_concat_max_len = CAST(
    (SELECT SUM(LENGTH(hobbies)) + COUNT(*) * LENGTH(', ')
    FROM peoples_hobbies 
    GROUP BY person_id)
    AS UNSIGNED
);