The files you're starting with are Gerber files, not the Proteus design file.
I don't know Altium or if it can import Gerber layers, but it looks like it might. You just have to help it understand which layer is which. There are different naming conventions; a commonly used one uses different file extensions to differentiate the layers. Typical names follow the pattern filename.xxx, where xxx equals the followimg:
GBL - bottom copper
GBO - bottom silkscreen
GBM - bottom solder mask
GBP - bottom solder paste
GTL - top copper
GTO - top silkscreen
GTS - top solder mask
GTP - top solder paste
GKO or GML - mechanical layer (board outline, milling, etc)
TXT - Excellon drill file.
Check how Altium differentiates the layers and rename them accordingly or see how to map from your names to what it wants.