The way construct exports the linux version does not cooperate with the steam web upload page because of the directory hierarchy
As of the latest Construct releases, when you choose to export to a single platform (e.g. just x64), it should place everything in the root level of the zip - there is no subfolder and so no need to unzip and re-zip.
I'm not sure what else to say - whenever I test this it works for me. There must be something you're doing wrong or some configuration is different on your end, but I don't know what that could be. Maybe it would be best to go to Valve for further support.