That a chess game occurred between two specific players on a specific date at a particular event is a fact. The moves that were made are facts. Facts are not protected by copyright, although particular words used to describe facts may be protected.
What books, databases, or other sources report a given game is a fact, and not protected unless the source constitutes a single selected list. If the book is 50 Best Chess Games selected by Joe Expert, then listing which games are included amounts to copying that selected list of games.
Annotations to or comments on a particular game would be protected by copyright, and may not be reproduced without permission unless they are old enough for copyright to have expired, or fit an exception to copyright. The fair use exception might or might not apply in the US, depending on the details and the use made, but would not apply elsewhere. The news reporting exception would not apply, I think.
The selection of a particular set of games as "notable" or "best" would be protected by copyright. Selecting such games as a set, or indicting which games belonged to such a list would be infringement. Including some such games along with many others, and in no way indicating which belonged to such a list would probably not be infringement of the copyright on the list.
A website or open database that provides data on such games may well have a TOS limiting how a user can access or use the data. For instance data scraping may be prohibited. Commercial use may be prohibited or restricted. Such a TOS probably forms a contract with each user, and any user is bound to its terms. Use of the site contrary to the TOS may be a breech of contract, and thus grounds for a lawsuit. What damages might be available would depend on the terms of the TOS, and the laws of the country where such a suit might be brought. That could include the country where the site is hosted, the country where the site owner does business, or where the user lives or works. In some countries, such as the US, Canada, or India, state or provincial laws might apply.
In some countries there is a "database right" similar to a copyright, that protects the data in a database as a collection. This can make it unlawful to copy subsets of data without permission, even if each individual datum is a fact not protected by copyright.
Games transcribed from a book would not raise the TOS or database rights issues.
That your proposed solution would be open-source does not make much difference to the rights of others who currently hold the data you want to access, whether under copyright, or contract, or database right. Being open source does not give any greater rights to access the works of others.
You might well want to consult a lawyer with IP knowledge in your country of residence for advice on the issues involved, particularly the database rights and TOS issues.