I replied to your solution with the two executeables. And I did look at the op creators page. There is a game that is in the tool category. At least the description reads like a game. It definityl does not read like a description for a tool. At least not what I would call a tool. There is possibilty that it is meant as a helper app for some esoteric rl stuff. It has local multiplayer tagged ;-)
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The role of launcher is done by the itch app, if you add another launcher you complicate the experience for the end user a bit and break the concept of launching the game through the itch app.
The idea of having 2 executables is to minimize that problem.
You run the setup only the first time, and subsequent times will launch the game, which is what the end customer expects when using the itch app.
Of course this is just one possible solution, there are many others and as you mention, another approach would be to have a single executable that acts as launcher and application.