You need to turn the question backwards. Instead of:
Which users have all of these tags, you need to ask which users do not have one or more of these tags absent. It's a double negation.
You also need a way to pass the set of tags. The best way to do this, if the client language binding supports it, is as an array-valued query parameter. If the client binding doesn't support array-valued parameters you'll need dynamic SQL.
One formulation might be (untested, since you didn't provide sample schema and data):
SELECT pl.email
FROM gameday.player_settings pl
WHERE NOT EXISTS (
SELECT 1
FROM unnest(?) AS wanted_tags(tag)
LEFT JOIN admin.tags tags
ON tags.tag = wanted_tags.tag
WHERE tags.player_id = pl.id
AND wanted_tags.tag IS NULL
);
Doing a left join and filtering for IS NULL is called a left anti-join. It keeps the rows where the left-join condition does not match. So in this case, we retain a tag from our wanted_tags array only if there is no matching tag associated with this player. If any tags are left, the WHERE NOT EXISTS returns false, so the player is excluded.
Double-think, isn't it? It's easy to make mistakes with this so test.
Here ? should be your programming language PostgreSQL database binding's query parameter placeholder. I don't know what node.js's is. This will only work if you can pass an array as a query parameter in node. If not, you'll have to use dynamic SQL to generate an ARRAY['x','y','z'] expression or a (VALUES ('x'), ('y'), ('z')) subquery.
P.S. Please provide sample schema and data with questions when possible. http://sqlfiddle.com/ is handy.
