Chess 2013 records the moves in the standard chess notation and lets you jump to any point in the game. It is a shareware game application that's modern.
Here are some screenshots to illustrate the features and user interface of this application:
Pit Your Wits in Chess 2013. Screenshot of Chess 2022 - 816px · 560pxFun chess game with many features. Screenshot of Chess 2022 - 816px · 560px