This guy - let's just call it simply HMC - is a so-called flavonoid (flavonoids are natural things found it lots of fruits and vegetables). Hesperidin, in particular, is a flavonone and is found in citrus fruits. The methylation of hesperidin gives HMC, that has well-established blood vessel protecting properties and can be found in drugs that treat problems related to blood vessels.
As for skincare, there is a mouse study showing HMC has very promising abilities in the "treatment of UVB irradiation-induced skin inflammation and oxidative stress", or English translation = it's an antioxidant and anti-inflammatory.
HMC is also part of a 3 active ingredient complex called Eyeliss (with Dipeptide-2 and Palmitoyl Tetrapeptide-7), that's supposed to fight under-eye bags. The manufacturer claims that in their ex-vivo test HMC decreased capillary permeability by 25%.
All in all, HMC definitely deserves a goodie status, at least as an antioxidant but it might even do something with under-eye bags.
- Chemico-Biological Interactions, 25 February 2015, Protective effects of the flavonoid hesperidin methyl chalcone in inflammation and pain in mice: Role of TRPV1, oxidative stress, cytokines and NF-κB
- Journal of Photochemistry and Photobiology B: Biology, Jul 1, 2015, Hesperidin methyl chalcone inhibits oxidative stress and inflammation in a mouse model of ultraviolet B irradiation-induced skin damage