Checked the link you listed, but Harbor Freight site indicates that number is invalid. I looked at the equipment they offered for sale and didn't see any with the capability to weld aluminum in the stock configuration.

I'm not sure of your level of knowledge of aluminum welding, but you need a power supply with A/C output, equipped with high frequency for starting and cleaning of metal as you weld.
Also required is a regulated supply of shielding gas, usually argon for aluminum. Most dedicated TIG machines will have these features as standard equipment. High frequency converters are available for machines without that feature and the regulated supply of shielding gas can be as simple as a gas bottle with a flow valve plumbed direct to the torch.

Since you're handy with a gas torch, you might like to know that aluminum was welded with that process until the invention of TIG. The use of an oxygen/hydrogen mix is preferred and a flux is applied to the welding rod during the process.

Good luck!

DT56