Lacquerware- http://mocoloco.com/chess-set-by-alexander-gelman/
Name of this style of chess pieces?

pretty sure looks like battalion style also seen in the pure chess game.
https://www.google.com/search?q=battalion+chess+set&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjgqsDG6pbVAhVM_IMKHSpEDuYQ_AUICygC#tbm=isch&q=pure+chess+batalion+chess+set&imgrc=Wdqw1cTAts6aAM:
Reminds me of art deco!
http://www.luxuo.com/the-lux-list/collectibles/alexander-gelman-chess-sets.html

Lacquerware- http://mocoloco.com/chess-set-by-alexander-gelman/
My original post wasn't put in the clearest way. Lacquering is the production process, I'm interested in what the figurative shape of the chess pieces is known as.
As an analogous examples, the ''Isle of Lewis'' and Staunton are the names of other figurative piece designs .
I would still really like to find the answer to this question.
You wrote two styles for an example, but both of these are named more than a hundred years ago. "Your" figures are made original specially and recently, it is too early to call it a separate direction in the design of chess.
I propose to look for analogies in architectural styles. All modern forms can be characterized by already known definitions.
In those chess - the form of brutalism and art-deco coverage (thanks for the opinion of anamorphosis64).

Possibly they may not have a name, however, they are not original as they feature in the Gelman example, as well as a set owned at least since 2001 (probably much earlier) by someone I know. In fact, it's the set I was taught to play chess on. It's unlikely two people individually designed pieces the exact perfectly same way, which is what lead me to open this thread. Originally I searched for other examples of the design, as obviously these two examples must stem from somewhere, but I can't find anything apart from Gelman's.
.. Topic related ; Including, an article embedded, "YouTube" link, of the home-made-tooling, of a 'modernist' art-style, wooden chess set.
http://lumberjocks.com/projects/329353
Recently I saw an article of a luxury chess set, imaged here, by a guy named Gelman

Gelman used some special crafting techniques, however, I believe the style of pieces is fairly well known and I have seen it before. Does anyone know what the name of the styling of chess pieces is called? Or can find a similar set somewhere on the internet?