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From what I've asked around and gathered so far: Saikyo Jump is a Japanese manga publication for young boys which exists primarily to sell toys and licensed products. As of yet, no known licensed products for Beast Saga have been announced. It is not explicitly obvious if Takara/Tomy/etc. are in any way involved. It is not known what, if any, toys may be made for it. For all we know it could be some weird mutation like what the newer Ultimate MUSCLE was of the original MUSCLE/Kinnikuman mini figures.
The character designs are tough to make out, but a red-armored green-maned lion looks unquestionably Battle Beasts/Beastformers-esque complete with a swell faction logo on his chest.
Special thanks to Zac for his insights and to Sylvain for emailing me to let me know about this new publication.