The structure is very similar to the other carotinids you mentioned- it has
a single hydroxyl group on one end connected to a ring, but otherwise the
molecule looks quite similar and very probably has similar effects.

The antioxidant function of carotinids lies in their unsaturated chains
(those get oxidized by radicals and thus prevent the unsaturated fatty acids
of the membranes to get oxidized) and cryptoxanthin has the same unsaturated
chain. So I supposed it will work as an antioxidant.

Just found an article on it as well:

Effect of carotenoids and ascorbic acid of Japanese persimmons on cellular
lipid peroxidation in HepG2 cells

Keisuke Hosotani A1, Atsushi Kawahata A1, Kanako Koyama A1, Chikako Murakami
A2, Hiromi Yoshida A2, Ryoichi Yamaji A3, Hiroshi Inui A3, Yoshihisa Nakano
A3

A1 Faculty of Education, Wakayama University, Wakayama, Japan
A2 Faculty of Nutrition, Kobe Gakuin University, Kobe, Hyogo, Japan
A3 Department of Applied Biological Chemistry, Osaka Prefecture University,
Sakai, Osaka, Japan

Abstract:

In this experiment, we examine the functional property of carotenoids;
?-cryptoxanthin (Cry), zeaxanthin (Zea), ?-carotene (Car)) and ascorbic acid
(AsA). The accumulation amounts of Cry, Zea and Car in HepG2 cells cultured
in the high concentration medium were larger than that in a low
concentration. Further those accumulation amounts in long incubation time
within 24~hours were greater than that in a shorter time. When the added
carotenoid concentration, with or without hydrogen peroxide, increased from
0 to 5 ?M in the culture medium, the thiobarbituric acid reaction substance
(TBARS) values in the HepG2 cells decreased significantly (p < 0.05). The
decrease of TBARS values shows the antioxidative property of the
carotenoids. When AsA and Tocopherol(Toc) were added to the medium from 0 to
20 ?M, the TBARS values, with or without hydrogen peroxide, decreased
significantly with increasing concentrations of AsA and Toc respectively (p
< 0.05). The decreased amount of TBARS in 5 ?M Cry compared with control(0
?M) was the largest among 6 antioxidants (Cry, Car, Zea, Retinol(Ret), AsA,
Toc) used in this experiment.