To the best of my basic, somewhat casual understanding, yes it is a style in the Southern Praying Mantis group.
I've always noticed that this Chukka seems somehow different, maybe a romanisation on Chow Gar / Chu Gar, which are more mainstream SPM, or maybe a romanisation of Hakka, referring to the race of people?
I'm sure the chinese characters would clear that up to someone who could read them.
Phoenix eye fist is common in that group of styles, family styles from southern China, many with Hakka roots.
So, like you, I've noticed it seems to be presented a little differently, but I reckon it comes from the same stuff as SPM, more of less.
That's about the best I can offer.
Guangzhou Pak Mei Kung Fu School, Sydney Australia,
Sifu Leung, Yuk Seng
Established 1989, Glebe Australia