The prints created from the POD service are definitely considered Giclees.

Graphik Dimensions uses pigmented inks and they use a large format printer.

The prints are archival if a 100% archival paper type is chosen. 
See this FAQ:
Paper Choices for POD

What is a giclee print?

Giclee (pronounced "gee-clay"), is a highly sophisticated inkjet printing process that was introduced in the late 1980s. It’s so sophisticated, in fact, that it produces prints, which truly capture the artist's original intent. Even museums have realized the vast potential of this technology and have made giclee editions a permanent part of their collections, including the Metropolitan Museum of Art (New York), Museum of Modern Art (San Francisco) and Museum of Contemporary Art (Los Angeles) to name a few. These prints are created from high-resolution digital images, using the finest quality ink and paper stock available, resulting in color saturation and image detail capture that exceeds other types of image reproduction.

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