Hello A, welcome to the Microsoft community, I'll be happy to help you today;
I understand that game mode is not available on your system;
Initially, I recommend that you follow the instructions below:
Check for new updates on Windows Update:
1: Open the Windows 10 "Start" menu and select the "Settings" item.
2: then select the "Update and Security" option.
3: In the "Windows Update" section, click "Check for updates".
4: If there are no updates, the message "You are up to date" will be displayed.
5: if there is any pending system update, the message "Features update for Windows 10 ..." will be displayed, then click on the "Download and install" item to start the system update.
6: wait for the update download to finish and restart the PC, or schedule a restart to be able to finish the procedure.
Update apps from the Microsoft Store;
Open the store and click (...) in the upper right corner to access Downloads and updates;
Click Get Updates and wait for all apps to update;
Check if the game mode feature is now displayed in the settings;
Press Windows key + I and go to Games;
If game mode is available just activate it;
Also click Xbox Game bar and enable the feature;
If the game mode feature is still not available, follow the instructions provided by the video below:
https://www.youtube.com/watch?v=P_L_Hst_iEQ
I hope I have helped, see you soon!