WiX definitely supports x64! I got the same issue and that seems to be somehow a crazy issue as I also got it working for another solution for x86 and x64. So I compared the two solution files and figured out what was going wrong with the one not working.
GlobalSection(ProjectConfigurationPlatforms) = postSolution
{HERE-IS-STANDING-A-GUID}.Debug|x64.ActiveCfg = Release|x86
{HERE-IS-STANDING-A-GUID}.Debug|x64.Build.0 = Release|x86
{HERE-IS-STANDING-A-GUID}.Debug|x86.ActiveCfg = Debug|x86
{HERE-IS-STANDING-A-GUID}.Debug|x86.Build.0 = Debug|x86
{HERE-IS-STANDING-A-GUID}.Release|x64.ActiveCfg = Release|x86
{HERE-IS-STANDING-A-GUID}.Release|x64.Build.0 = Release|x86
{HERE-IS-STANDING-A-GUID}.Release|x86.ActiveCfg = Release|x86
{HERE-IS-STANDING-A-GUID}.Release|x86.Build.0 = Release|x86
EndGlobalSection
This is a generated nonworking one. To make it work, I replaced the first four strings behind the "=" and played a bit with doing an x86 and x64 build. That worked for me.
Here is the same but working code:
GlobalSection(ProjectConfigurationPlatforms) = postSolution
{HERE-IS-STANDING-A-GUID}.Debug|x64.ActiveCfg = Debug|x64
{HERE-IS-STANDING-A-GUID}.Debug|x64.Build.0 = Debug|x64
{HERE-IS-STANDING-A-GUID}.Debug|x86.ActiveCfg = Debug|x86
{HERE-IS-STANDING-A-GUID}.Debug|x86.Build.0 = Debug|x86
{HERE-IS-STANDING-A-GUID}.Release|x64.ActiveCfg = Release|x64
{HERE-IS-STANDING-A-GUID}.Release|x64.Build.0 = Release|x64
{HERE-IS-STANDING-A-GUID}.Release|x86.ActiveCfg = Release|x86
{HERE-IS-STANDING-A-GUID}.Release|x86.Build.0 = Release|x86
EndGlobalSection
Hope that works for you as well