Your query would be something like this:
SELECT game
FROM YourTable
WHERE EXISTS (SELECT 1 FROM UNNEST(participant) WHERE name = 'sam');
This returns all of the games where 'sam'
was a participant. Here is a self-contained example:
WITH YourTable AS (
SELECT 'A' AS game, ARRAY<STRUCT<name STRING, age INT64>>[('sam', 12), ('tony', 12), ('julia', 12)] AS participant UNION ALL
SELECT 'B', ARRAY<STRUCT<name STRING, age INT64>>[('sam', 12), ('max', 12), ('jacob', 12)] UNION ALL
SELECT 'C', ARRAY<STRUCT<name STRING, age INT64>>[('sam', 12), ('max', 12), ('julia', 12)]
)
SELECT game
FROM YourTable
WHERE EXISTS (SELECT 1 FROM UNNEST(participant) WHERE name = 'sam');
If you wanted to pivot the data to have a column for each participant, you could use a query like this:
CREATE TEMP FUNCTION WasParticipant(
p_name STRING, participant ARRAY<STRUCT<name STRING, age INT64>>) AS (
EXISTS(SELECT 1 FROM UNNEST(participant) WHERE name = p_name)
);
WITH YourTable AS (
SELECT 'A' AS game, ARRAY<STRUCT<name STRING, age INT64>>[('sam', 12), ('tony', 12), ('julia', 12)] AS participant UNION ALL
SELECT 'B', ARRAY<STRUCT<name STRING, age INT64>>[('sam', 12), ('max', 12), ('jacob', 12)] UNION ALL
SELECT 'C', ARRAY<STRUCT<name STRING, age INT64>>[('sam', 12), ('max', 12), ('julia', 12)]
)
SELECT
ARRAY_AGG(IF(WasParticipant('sam', participant), game, NULL) IGNORE NULLS) AS sams_games,
ARRAY_AGG(IF(WasParticipant('tony', participant), game, NULL) IGNORE NULLS) AS tonys_games,
ARRAY_AGG(IF(WasParticipant('julia', participant), game, NULL) IGNORE NULLS) AS julias_games,
ARRAY_AGG(IF(WasParticipant('max', participant), game, NULL) IGNORE NULLS) AS maxs_games
FROM YourTable;
This returns an array with games played for each participant.