I was able to deduce an answer by 'reverse-engineering' (sort of) the default
filter:
/2.2/filters/default
this gives
{
"items": [
{
"included_fields": [
".backoff",
".error_id",
".error_message",
".error_name",
".has_more",
".items",
".quota_max",
".quota_remaining",
"access_token.access_token",
"access_token.account_id",
"access_token.expires_on_date",
"access_token.scope",
"account_merge.merge_date",
... many lines omitted ...
"user_timeline.user_id",
"write_permission.can_add",
"write_permission.can_delete",
"write_permission.can_edit",
"write_permission.max_daily_actions",
"write_permission.min_seconds_between_actions",
"write_permission.object_type",
"write_permission.user_id"
],
"filter_type": "safe",
"filter": "default"
}
],
"has_more": false,
"quota_max": 10000,
"quota_remaining": 9944
}
It becomes obvious that you must fully specify each field in the method call. The call in the question becomes
/2.2/filters/create?include=site.api_site_parameter;.items&base=none
which, when used with /2.2/sites
, gives
{
"items": [
{ "api_site_parameter": "stackoverflow" },
{ "api_site_parameter": "serverfault" },
{ "api_site_parameter": "superuser" },
{ "api_site_parameter": "meta" },
{ "api_site_parameter": "webapps" },
{ "api_site_parameter": "meta.webapps" },
{ "api_site_parameter": "gaming" },
{ "api_site_parameter": "meta.gaming" },
{ "api_site_parameter": "webmasters" },
{ "api_site_parameter": "meta.webmasters" },
{ "api_site_parameter": "cooking" },
{ "api_site_parameter": "meta.cooking" },
{ "api_site_parameter": "gamedev" },
{ "api_site_parameter": "meta.gamedev" },
{ "api_site_parameter": "photo" },
{ "api_site_parameter": "meta.photo" },
{ "api_site_parameter": "stats" },
{ "api_site_parameter": "meta.stats" },
{ "api_site_parameter": "math" },
{ "api_site_parameter": "meta.math" },
{ "api_site_parameter": "diy" },
{ "api_site_parameter": "meta.diy" },
{ "api_site_parameter": "meta.superuser" },
{ "api_site_parameter": "meta.serverfault" },
{ "api_site_parameter": "gis" },
{ "api_site_parameter": "meta.gis" },
{ "api_site_parameter": "tex" },
{ "api_site_parameter": "meta.tex" },
{ "api_site_parameter": "askubuntu" },
{ "api_site_parameter": "meta.askubuntu" }
]
}