It is a fact that a particulate chess game was played on a particular date by certain specific players, who made specific moves. Facts are not protected by copyright. Anyone is free to report such a game, including the exact moves, and the names of the players. Such games are often used in books about chess, and the same thing is done in books about other games, such as bridge and go, where a record of the play is often kept.
If someone else has described or analyzed such a game, you may not copy that person's wording without permission (except to the limited extent permitted by fair use or fair dealing).
A chess diagram simply represents the position of the pieces in a standard way, and has no original content beyond those facts, and so is not protected by copyright either.
If a person has invented a chess game or a series of chess moves that never took place to illustrate a point in analyzing chess, re-using that sequence of moves might make the new analysis a derivative work of the previous one, if the coverage of the invented sequence of moves is extensive. But that would not apply to the moves of an actual game that was actually played.
There have even been cases of fictional stories based upon real historical chess games. For example "Unicorn Variation" by Roger Zelezney.
17 USC 102 says:
In no case does copyright protection for an original work of authorship extend to any idea, procedure, process, system, method of operation, concept, principle, or discovery, regardless of the form in which it is described, explained, illustrated, or embodied in such work.
This is the "fact/expression distinction" by which it is said that facts are not protected by copyright, although the form of expressing those facts often is. The same section has the list of kinds of protected works. This includes literary, dramatic, musical, and pictorial works, dance, audiovisual, sound and architectural works. A chess game does not fall into any of those categories. Thus it is ineligible form protection on two separate but related grounds. Beyond that, under the Feist vs Rural decision, a work must have an element of originality to be protected by copyright, and a list of the moves made by chess players has no original content, although an analysis of a game would. The copyright laws of many other countries have been interpreted similarly.
As to the question of offense, in the US at least, and in most other countries, a true statement is never legally defamatory, even if the subject dislikes it. If it is true that Player X lost to Player Y on such and such a date, reporting that fact cannot be libel or any form of defamation. Otherwise the loser could never be named in any sports reporting.