My question is that I see that there are different HDMI specs like 1.1, 1.2, and 1.3. Do these specs only apply to devices such as TV's, Blu-ray Players, and AV Receivers or are there also different versions of HDMI cables (like 1.1, 1.2, and 1.3)?

They do, sort of apply to cables, but it isn't hugely relevant. Some of the newer features provided by newer HDMI specs may allow for higher bandwidth transmission which my be more problematic particularly with distance runs, but if the bandwidth is high enough it doesn't matter what number "version" is on the HDMI cable as long as it has the performance to support that bandwidth.

In other words, like the differences in category cabling, if the bandwidth is high enough or the distance short enough, there is no reason an old Cat5 cable may not work fine for gig ethernet. But it depends on what the capabilities of the particular cable in question.