These aren't sequels or side stories pretending to matter. They're the show letting its hair down after proving it could build something real. Four episodes of Kenichi and his dojo family existing outside the tournament grind, which means the comedy lands harder because you actually care about these people taking hits. The action still moves like it knows what it's doing. This is what bonus content should be: an extension that understands why you showed up in the first place, not filler that tests your patience.
Kenichi's new life at Ryouzanpaku gets a short recap in these four specials, which blend action and comedy. They were released as bonus extras on the DVD volumes of the Shijou Saikyou no Deshi Kenichi OVAs, so they work as brief companion pieces to those episodes rather than standalone stories.