groonga/en

Umm. It's too rough instruction. I couldn't reproduce your case with the instruction.
I try the following and it works well:

1.Install PostgreSQL 11.3 by installer: https://www.enterprisedb.com/thank-you-downloading-postgresql?anid=1256619

1. Download PGroonga binary for PostgreSQL 11: https://github.com/pgroonga/pgroonga/releases/download/2.1.9/pgroonga-2.1.9-postgresql-11.2-1-x64.zip
2. Extract the PGroonga binary to C:\Program Files\PostgreSQL\11 (I needed to enable administrator permission)
3. I run psql from startup menu
4. Connect to postgres database with postgres user
5. Create pgroonga_test database by CREATE DATABASE pgroonga_test;
6. Change database by \c pgroonga_test
7. Install PGroonga by CREATE EXTENSION pgroonga; (It doesn't report any error)
8. Run the following SQL in tutorial https://pgroonga.github.io/tutorial/

CREATE TABLE memos (
  id integer,
  content text
);
CREATE INDEX pgroonga_content_index ON memos USING pgroonga (content);
INSERT INTO memos VALUES (1, 'PostgreSQL is a relational database management system.');
INSERT INTO memos VALUES (2, 'Groonga is a fast full text search engine that supports all languages.');
INSERT INTO memos VALUES (3, 'PGroonga is a PostgreSQL extension that uses Groonga as index.');
INSERT INTO memos VALUES (4, 'There is groonga command.');
SET enable_seqscan = off;
SELECT * FROM memos WHERE content &@ 'engine';
--  id |                                content                                 
-- ----+------------------------------------------------------------------------
--   2 | Groonga is a fast full text search engine that supports all languages.
-- (1 row)

So, it will be your environment specific issue.