You could but I think calling it a "variation" would fit more. If you want to create your own board game, you'll need a new unique idea to even get pass the costs of the materials and tools, alone beginning to create it
I was thinking, how would one go about inventing another game like Chess.

OK I have invented/designed a whole new genuine idea. Its kinda like chess, but also kinda like backgammon. Its very new and needs more play testing. Look here fo0r the latest Video of basic rules. The game is called TRAIDERS of the STAR https://youtu.be/4ap7qn95y7E

Decide if the game will involve armies, mythical creatures, or abstract pieces like chess.
Decide on the basic rules of movement, capture, and special abilities of the pieces. This is where you'll make the game distinct from chess.
Consider factors like board size, starting positions, and any special zones or areas on the board.
Playtest extensively to refine the rules and mechanics. This can be done with friends, family, or through playtesting groups.
Determine how the game is won. Is it by capturing a particular piece, controlling a specific area, or achieving a certain goal?
that's why I love the game of chess ...no game in earth can be compared to chess ...chess is simply sweet
shogi?