Your gallery does not explicitly set captionHAlign="LEFT" (there is no sign of this configuration option in your gallery's 'config.xml' file) so the gallery should be using the default value for captionHAlign (which is LEFT anyway).
However, your captions are being centered due to custom CSS in your 'style.css' file, specifically line 63:

td {text-align: center; vertical-align:middle;}

This will center-align text in all <td> elements on your web page (including those on your gallery's caption area).
It is not possible to isolate a Juicebox gallery (or any other HTML element) from global CSS and the gallery has no option but to inherit such rules.
The best course of action would be to have custom CSS rules applied to only those elements on your web page which require them through use of further CSS selectors (classes and ids).

Another possible solution would be to add the following CSS to your web page. It should solve your problem and align your gallery captions LEFT but it may prevent captionHAlign from working with any other value. The better solution is to apply your own custom CSS rules to only those elements on your web page that require it (rather than to all <td> tags).

.juicebox-gallery td {text-align: left !important;}