If you read the Driver name for the Touch pad under the Windows 10 64-bit section, it looks like a 32bit driver:
Dell Touchpad Driver View details
Input_Driver_CN4KX_WN32_19.0.9.4_A00.EXE | Update Package for Microsoft® Windows® (62 MB)
Mouse, Keyboard & Input Devices|Release date 30 Jul 2015|Last Updated 31 Jul 2015|Recommended
Version 19.0.9.4,A00
Attention on the name "INPUT_DRIVER_CN4KX_WN32". Have you given it a shot? I understand you've tried the Windows 7 already. Won't hurt giving this one a shot.