As indicated by the
table linked on that page VS Express does include a compiler that can target x64 architecture. It does
not include a 64-bit toolchain. In other words, it can make 64-bit programs but it itself is not a 64-bit program.
The page you linked is about switching the 32-bit compiler for 64-bit compiler, not about making 64-bit programs.
To build a 64-bit program, you need to make a new project and solution configuration that targets x64. To do this, click the dropdown for selecting debug/release and click the "Configuration Manager..." option. Then click the dropdown under "Active solution platform" and select "<New...>". Then select "x64" from the top dropdown, and pick a platform to copy settings from. Make sure "Create new project platforms" is checked. Then you'll be able to set up and build for both 32-bit and 64-bit programs.
(Instructions are from MSVC 2013 Pro, as I don't have Express on hand, but it should be the same or similar)
Converting a project to build for x64 by hand is harder, as you'll have to fix up all the library paths, settings, and preprocessor settings to build for x64.
Whether or not you need to make a 64-bit app is a whole other discussion, as most indie games and personal projects won't get any advantage.
Edit: Ironically, the instructions that I just typed up are listed
on MSDN right above the page you posted on the left-hand sidebar.