Is it possible to clean up duplicate entries with just SQL?
Your data sample seems to suggest that the two datetime columns are the only columns that can change in each group of duplicates. In other words, duplicates are determined by columns player_id, season_id, playlist_id, matches_played, rank_points, tier, division.

One other assumption that your data sample prompts is that a row with a greater timestamp corresponds to a row with a greater no_update_at as well. (In fact, the two columns always have the same value in your example.)

Finally, for the purpose of this answer, I am also going to assume that when you are saying "first" or "last" (row in the rectangle), you are talking about the earliest or latest datetime value.

With those out of the way, you can generate the desired result set from your table if you just group the rows by the columns listed above and take MIN(timestamp) for timestamp and MAX(no_update_at) for no_update_at – that is, like this:

SELECT
  player_id,
  season_id,
  playlist_id,
  MIN(timestamp) AS timestamp,
  matches_played,
  rank_points,
  tier,
  division,
  MAX(no_update_at) AS no_update_at
FROM
  graph_player_ranked
GROUP BY
  player_id,
  season_id,
  playlist_id,
  matches_played,
  rank_points,
  tier,
  division
;


You could store that in a temporary table:

CREATE TEMPORARY TABLE tmp_graph_player_ranked
AS
SELECT
  ...
;


then truncate the source:

TRUNCATE graph_player_ranked;


and populate it from the temporary table:

INSERT INTO
  graph_player_ranked
    (
      player_id,
      season_id,
      playlist_id,
      timestamp,
      matches_played,
      rank_points,
      tier,
      division,
      no_update_at
    )
SELECT
  player_id,
  season_id,
  playlist_id,
  timestamp,
  matches_played,
  rank_points,
  tier,
  division,
  no_update_at
FROM
  tmp_graph_player_ranked
;


Of course, if the table is referenced by other tables, you cannot simply remove all data – you will probably need to disable or remove the foreign keys before re-populating the table and enable or recreate them afterwards. (That is an entirely different problem that would need to be addressed separately, in case you need help with it.)