There are plenty of websites offering the very same items of jewellery at a variety of prices on the internet. Trying to substantiate the authenticity of these suppliers isn't easy but there are enough reasons to be wary of some of them. I'm not going to go through them all because that's impractical.
As regards drop shipping, which was the substance of the OP's original question, then the same basic principles apply to this as to any similar offer. You have to know the company/person offering you the deal and be able to check on their track record because, at the end of the day, it's your bank account that will bear the cost of any failings or errors. As much as you could earn money, you could also lose a lot of money if orders aren't satisfied.
In this instance, as the company offering the deal doesn't disclose their identity on their website, and it's a foreign company with no traceable track record, acting as drop shipper for them would be risky. This is not to say that they aren't respectable and trustworthy, there simply isn't any means to confirm this. On the same basis my bank manager doesn't lend to strangers.
The likelihood is that a buyer of diamond jewellery is going to want to see any items they buy before making a purchase, moreso than even someone buying a used automobile. I would never make the mistake of buying an item of jewellery for a loved one online, even from a known company, and I suspect that part of the purchase experience for a female is being able to try and compare items.
Using eBay sellers with track records may be one way to partially get over the resistance of buyers who prefer to deal with sellers with a track record, but it doesn't address the problem of people wanting to see and touch the product. Meanwhile the seller bears the risk if the buyer is not satisfied.
I also note that a lot of the diamonds offered for sale are referred to as 'clarity enhanced'. Obviously I have no knowledge of the significance of this but it appears that it does have legal implications as regards anyone selling them.
https://en.wikipedia.org/wiki/Diamond_enhancementDiamond enhancements are specific treatments, performed on natural diamonds (usually those already cut and polished into gems), which are designed to improve the visual gemological characteristics of the diamond in one or more ways. These include clarity treatments such as laser drilling to remove black carbon inclusions, fracture filling to make small internal cracks less visible, color irradiation and annealing treatments to make yellow and brown diamonds a vibrant fancy color such as vivid yellow, blue, or pink.
The CIBJO and government agencies such as the United States Federal Trade Commission explicitly require the disclosure of all diamond treatments at the time of sale. Some treatments, particularly those applied to clarity, remain highly controversial within the industry — this arises from the traditional notion that diamonds hold a unique or "sacred" place among the gemstones, and should not be treated too radically, if for no other reason than a fear of damaging consumer confidence.
Clarity and color enhanced diamonds sell at lower price points when compared to similar, untreated diamonds. This is because enhanced diamonds are originally lower quality before the enhancement is performed, and therefore are priced at a substandard level. After enhancement, the diamonds may visually appear as good as their non-enhanced counterparts. Therefore, treated diamonds appear to have a greater value than they would before treatment, but whether this is in fact the case is questionable.
Overall though I believe that the main problem is that the majority of the public aren't ready to buy diamond jewellery online.