For those people that want to run the game in linux I have two options:
Via STEAM:
In Steam at the top left corner, click Games you will see Add a Non-Steam game to my Library.
At the bottom of the new window there's browse, click that.
Now navigate to the folder where your game is at and select the English Launcher.exe or the other Launcher.exe.
Then Open.
It should lead you back to the first window, with the Add Selected Programs now showing up (you can also verify by scrolling the list), click that.
Now the game is in your library, find the game and right click it.
Go to Compatibility and Force the use of a specific Steam Play compatibility tool.
Choose Proton, the one I used was specifically Proton 10.0-3
Then go back to the Shortcut and type this in launch options, "WINEDLLOVERRIDES="winhttp=n,b" %command%"
This launch command makes it so that the English Launcher launches you into the English Translated Menus otherwise everything would still be in japanese.
That's it you're good to go.
Via Lutris:
Open Lutris.
Click the + at the top right. Then click Add locally installed game.
Set the name, I set mine to Summer in Heat - English Launcher.
Then choose Runner to be Wine.
Then move to Game Options for the executable find the English Launcher.exe or the other Launcher.exe.
This part is important because this is where I initially failed, the Wine Prefix.
For this you're gonna have to create a random folder somewhere(would be better if it's close to your game directory), for me I created two for cleanliness.
I created GamesPrefix folder and inside that folder I created SummerInHeat.
Then going back to Game Options we're now going to navigate to the newly created SummerInHeat folder and select the empty folder as the Wine Prefix.
Set Prefix Architecture to 64-bit.
Then we move on to Runner Options.
Don't change anything here and go to the bottom where you'll see DLL overrides, click the add button at the bottom right.
It should create a new row, the key is "winhttp" and value is "n,b".
Then save.
You should be good to go.