Although I could not understand how to do this in the Install Shield LE client (and could not get help from Flexera support, because it is a free product), I figured out how to do it.
As pointed out in my question, there is no “Template Summary” property in the client user interface:

However, I found that this property exists in the .ISL file. Opening this in a text editor and replacing intelwith one x64works:
<template>x64;1033</template>
:, "stick", Visual Studio, .