Postgres hasn't implemented an equivalent to INSERT OR REPLACE. From the ON CONFLICT docs (emphasis mine):

It can be either DO NOTHING, or a DO UPDATE clause specifying the exact details of the UPDATE action to be performed in case of a conflict.

Though it doesn't give you shorthand for replacement, ON CONFLICT DO UPDATE applies more generally, since it lets you set new values based on preexisting data. For example:

INSERT INTO users (id, level)
VALUES (1, 0)
ON CONFLICT (id) DO UPDATE
SET level = users.level + 1;

According to the Postgres documentation https://www.postgresql.org/docs/current/sql-insert.html the INSERT INTO statement has two WHERE conditions:

1. ON CONFLICT ... WHERE index_predicate in the conflict_target part. Postgres needs to understand on what unique index it should react to conflicts, especially if you have multiple unique indexes on a table. You can specify the exact index name, or you can specify column name and other parameters and Postgres will try to find ("infer") corresponding index. The index_predicate allows to infer partial unique indexes (i.e. unique indexes that contain information only about part of the table), but any indexes that satisfy the predicate (not only partial indexes) can be inferred.
2. DO UPDATE SET ... WHERE condition in the conflict_action part. Only rows for which this condition expression returns true will be updated.

So you need to move you WHERE clause from the ON CONFLICT block to the DO UPDATE SET block:

CREATE TABLE books (
    id int4 NOT NULL,
    version int8 NOT NULL,
    updated timestamp NULL,
    CONSTRAINT books_pkey PRIMARY KEY (id)
);

INSERT INTO books VALUES (12, 0, CURRENT_TIMESTAMP)
ON CONFLICT (id) 
DO UPDATE SET version = books.version + 1, updated = CURRENT_TIMESTAMP
WHERE books.version IS NULL OR books.updated + INTERVAL '2min' < CURRENT_TIMESTAMP;

Upd: In your case the version cannot be NULL and you don't need the books.version IS NULL condition. In case you need to allow NULLs be aware that NULL + 1 will be NULL (thanks @dwhitemv for noticing) so you will need to modify the SET statement using COALESCE or conditions.