How to select unique records in PostgreSQL without using Distinct clause
A query that may get the "desired output" could look something like this:
(as @joanolo had suggested: adding the second and third column to the GROUP BY)

select
  R.house
, R.id rows_
, R.points
from jkrecords R
group by R.house, R.id, R.points
order by R.house, R.id;


See a worked example here.
Apologies to everyone, and to @a_horse_with_no_name in particular, for any confusion I may have caused with my "assumptions".