How to query for certain text in log messages from Google App Engine that are exported to BigQuery?
The reason why this query failed is because you have a table with nested repeated field protoPayload.line (datatype RECORD).  

You can try implicit unnesting, it would be something like: 

SELECT x
FROM `gae_log.appengine_googleapis_com_request_log_20180323` as t, 
      t.protoPayload.line AS x
WHERE x.logMessage  like '%14994838999176%'


You can also have a look on how to query STRUCT elements in an ARRAY here.