[Fire HD 8 and HD 10 Q&A, Help & Troubleshooting] sega dude:
Is there a way to enable Game mode for non-Amazon App Store games? Games downloaded from the Amazon App Store automatically activate Game Mode when they are opened. Game Mode actually seems to help because games downloaded from the Amazon App Store perform significantly better than the same game downloaded from the Play Store. As a result, I always download the game from the Amazon App Store if it is available there. Does anyone know how Game Mode is activated? I'm thinking it's something in the manifest of the APKs that come from the Amazon app store. I want to figure out to activate it for games from Google Play. I have a Fire HD 10 2019.

Edit 5/8/2021 -

I started a game from the Amazon App Store while connected to ADB and this is what I got. These lines did not appear until after I hit the OK button on the Game Mode prompt. Maybe this will help someone figure it out.

2021-05-08 15:12:53.432 627-763/? D/GameModeService: Entering GameMode!
2021-05-08 15:12:53.436 627-763/? I/GameModeAlexaCallback: onGameModeStateChanged() | setting in_game_mode = 1
2021-05-08 15:12:53.461 970-970/? I/AmazonSystemUIGameModeManager: GameModeEventListener.onStateChange() | currentState: STATE_DEVICE_ENTERED_GAME_MODE
2021-05-08 15:12:53.493 627-763/? I/ActivityManager: Killing 25768:com.teslacoilsw.launcher/u0a57 (adj 600): GameMode killAllBackgroundProcesses
2021-05-08 15:12:53.524 627-763/? I/ActivityManager: Killing 23331:com.amazon.alta.h2clientservice/u0a99 (adj 800): GameMode killAllBackgroundProcesses
2021-05-08 15:12:53.531 627-763/? I/ActivityManager: Killing 27321:com.amazon.webview.chromium:AWVMetricsProcess/u0a152 (adj 800): GameMode killAllBackgroundProcesses
2021-05-08 15:12:53.539 627-763/? I/ActivityManager: Killing 27393:com.android.vending/u0a41 (adj 901): GameMode killAllBackgroundProcesses
2021-05-08 15:12:53.548 627-763/? I/ActivityManager: Killing 23982:com.amazon.alexa.multimodal.gemini/u0a175 (adj 800): GameMode killAllBackgroundProcesses
2021-05-08 15:12:53.558 627-763/? I/ActivityManager: Killing 2462:com.amazon.kindle.cms/u0a120 (adj 500): GameMode killAllBackgroundProcesses
2021-05-08 15:12:53.563 627-763/? I/ActivityManager: Killing 25585:com.google.android.gms/u0a38 (adj 0): GameMode killAllBackgroundProcesses
2021-05-08 15:12:53.568 627-763/? I/ActivityManager: Killing 24259:com.perpendox.phem/u0a226 (adj 800): GameMode killAllBackgroundProcesses
2021-05-08 15:12:53.572 627-763/? I/ActivityManager: Killing 29989:com.android.proxyhandler/u0a96 (adj 200): GameMode killAllBackgroundProcesses
2021-05-08 15:12:53.582 627-763/? I/ActivityManager: Killing 23615:com.android.email:Sync/u0a46 (adj 800): GameMode killAllBackgroundProcesses
2021-05-08 15:12:53.585 627-763/? I/ActivityManager: Killing 24326:com.amazon.whisperlink.core.android/u0a16 (adj 500): GameMode killAllBackgroundProcesses
2021-05-08 15:12:53.592 627-763/? I/ActivityManager: Killing 23811:com.amazon.comms.kids/u0a179 (adj 800): GameMode killAllBackgroundProcesses
2021-05-08 15:12:53.610 627-763/? I/ActivityManager: Killing 23572:com.android.email/u0a46 (adj 0): GameMode killAllBackgroundProcesses
2021-05-08 15:12:53.619 627-763/? I/ActivityManager: Killing 25723:com.helloka.worldtimebuddy/u0a203 (adj 901): GameMode killAllBackgroundProcesses
2021-05-08 15:12:53.622 627-763/? I/ActivityManager: Killing 23225:com.amazon.avod/u0a89 (adj 800): GameMode killAllBackgroundProcesses
2021-05-08 15:12:53.629 627-763/? I/ActivityManager: Killing 23438:com.amazon.device.services/1000 (adj 800): GameMode killAllBackgroundProcesses
2021-05-08 15:12:53.635 627-763/? I/ActivityManager: Killing 1562:com.google.process.gapps/u0a38 (adj 700): GameMode killAllBackgroundProcesses
2021-05-08 15:12:53.639 627-763/? I/ActivityManager: Killing 8509:com.google.android.inputmethod.latin/u0a100 (adj 200): GameMode killAllBackgroundProcesses
2021-05-08 15:12:54.827 627-770/? W/Eve: MEMORY_LEVEL: [1445,-800]
top=com.limelight/.PcView launching=false
prev=com.teslacoilsw.launcher/.NovaLauncher screen_on=true thermal=0
adb=true downloading=false gamemode=true
memory=0 trim=0 available=0KB free=394836KB
2021-05-08 15:12:57.277 627-770/? W/Eve: MEMORY_LEVEL: [1445,-800]
top=com.limelight/.PcView launching=false
prev=com.teslacoilsw.launcher/.NovaLauncher screen_on=true thermal=0
adb=true downloading=false gamemode=true
memory=0 trim=0 available=0KB free=254400KB
2021-05-08 15:12:59.285 627-770/? W/Eve: MEMORY_LEVEL: [1445,-800]
top=com.limelight/.PcView launching=false
prev=com.teslacoilsw.launcher/.NovaLauncher screen_on=true thermal=0
adb=true downloading=false gamemode=true
memory=0 trim=0 available=0KB free=161436KB