I've figured out an example how to run without special support from this library, from the python bg tool's apilog (from the google-cloud-sdk), also from ./opt/google-cloud-sdk/platform/bq/bq.py source code (googleapis/google-cloud-python#2342 (comment) says the google-cloud-sdk is not open source, but you can read the source to see how queryParameters is constructed):

$ bq --apilog - query --use_legacy_sql=false --parameter arr:'ARRAY<INTEGER>':'[2,3,4]' 'SELECT 3 IN UNNEST(@arr)'
[...]

INFO:root:body: {"configuration": {"query": {"query": "SELECT 3 IN UNNEST(@arr)", "useLegacySql": false, "queryParameters": [{"parameterType": {"type": "ARRAY", "arrayType": {"type": "INTEGER"}}, "parameterValue": {"arrayValues": [{"value": 2}, {"value": 3}, {"value": 4}]}, "name": "arr"}]}}, "jobReference": ...}

INFO:root:{
 "kind": "bigquery#job",
 "etag": "...",
 "id": "...",
 "selfLink": "...",
 "jobReference": {
    ...
 },
 "configuration": {
  "query": {
   "query": "SELECT 3 IN UNNEST(@arr)",
   "destinationTable": {
      ...
   },
   "createDisposition": "CREATE_IF_NEEDED",
   "writeDisposition": "WRITE_TRUNCATE",
   "useLegacySql": false,
   "queryParameters": [
    {
     "name": "arr",
     "parameterType": {
      "type": "ARRAY",
      "arrayType": {
       "type": "INT64"
      }
     },
     "parameterValue": {
      "arrayValues": [
       {
        "value": "2"
       },
       {
        "value": "3"
       },
       {
        "value": "4"
       }
      ]
     }
    }
   ]
  }
 },
 "status": {
  "state": "RUNNING"
 },
 "statistics": {
  "creationTime": "1479104934691",
  "startTime": "1479104934979"
 },
}
INFO:root:--response-end--
+------+
| f0_  |
+------+
| true |
+------+

this is saying:

parameterMode is optional: I can set it to 'positional' or 'named' but any other value results an error, but if not sending this, it's totally fine; you see bq tool is not sending parameterMode at all
it's also a good example of how ARRAY type should be sent, it's in a recursive structure, from this I inferred how to construct a STRUCT type and it works

or saying if I am doing queryParameters in this structure on myself, that just works fine, but maintainers of this library can make an API for users to use queryParameters easier

   "queryParameters": [
    {
     "name": "arr",
     "parameterType": {
      "type": "ARRAY",
      "arrayType": {
       "type": "INT64"
      }
     },
     "parameterValue": {
      "arrayValues": [
       {
        "value": "2"
       },
       {
        "value": "3"
       },
       {
        "value": "4"
       }
      ]
     }

bigquery: support SQL parameters #390

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