Is cheap Chinese labor really why we can get so many gadgets for Christmas?

The cost of production of many consumer goods are determined by a combination of efficiency in manufacturing (good) and unreasonable exploitation of workers and the environment (bad). Consumer pressure in the market can sometimes cause a temporary back-down, but as a whole I doubt it is very effective, simply because consumers can't easily differentiate products produced by workers getting fair pay and with appropriate environmental safeguards.

The most effective response would be for governments to set tariffs determined so that manufacturers who can't prove labour below a certain cost wasn't used (and other similar social and environmental measures), so manufacturers can't outsource to avoid laws that exist for the wellbeing of society.

These types of measures often meet opposition, because they get lumped in with overzealous protectionist policies because both are aberrations from the principle of free trade. However, the former are aberrations which are beneficial to the world economy, while the latter can be harmful. Separating the two types of measures legally is difficult; I think the best approach is to avoid free trade treaties, educate the public about the benefits of free trade done right and the pitfalls of it done wrong, and let each country unilaterally decide which tariffs are beneficial and which are harmful to impose on imports into that country.

I don't know that I see the point. Just because they could pay more doesn't mean that the fact that they don't doesn't enable a cheap consumerist society where we benefit off of their poor working conditions.