As to how this is possible, because of a new "paradox", it is now possible for Another Riders to appear alongside with their original counterparts with their history still intact. To put it simply, Blade and Chalice are fighting because of their nature as Joker Undead as the two are the last remaining Undead standing in the Battle Fight.
The Kamen Rider Blade Arc will cover episodes 29 and 30 of the TV series and will air on March 31st and April 7th respectively.
[Additional info: Oricon]