Kawakami's company had already produced Othello and The Merchant of Venice in 1903 before finally getting around to Hamlet; they were not time-wasters. On the other hand, NIKI Hisae characterizes their work as "sensational and melodramatic" and Kawakami himself as "a showman, who could not recognize the artistic value of the play." Ouch.
I haven't read any Kawakami-company scripts, but I have heard that, for example, the soliloquies were cut — even "to be or not to be" — so it seems fair to conclude that sensation and melodrama were prioritized over psychological portraiture. Kawakami also tended to modernize and localize the content of the plays: thus, Hamlet became a story set in contemporary Japan about Hamura and Orie instead of Hamlet and Ophelia.
Such shenanigans allowed TSUBOUCHI Shōyō to take the credit for the first modern performance of Shakespeare for his Bungei Kyōkai production of Hamlet later in the decade. What scholars mean by "modern" here is that it was a more or less faithful and complete translation, with no cut soliloquies (and absolutely no jōruri), plus the use of female actors for female parts — although, paradoxically, Shakespeare didn't do this (and Kawakami did).
Pioneering though it was, Shōyō's production had its critics. One of these critics was NATSUME Sōseki (for it is he), who wrote a typically crabby review for the papers in which he declared that "Shakespeare's plays, by their fundamental nature, do not permit translation into Japanese" (沙翁劇は其劇の根本性質として、日本語の翻訳を許さぬものである). If Shakespeare absolutely had to be translated, Sōseki went on, it should at least be done like a Noh play or something, reflecting the fact that Shakespeare's lines were poetry in an elevated style. (No idea if Sōseki was aware of Shōyō's jōruri Julius Caesar.)
Anyway, almost a century later, professor UEDA Kuniyoshi 上田邦義 took Sōseki's idea and ran with it. The result: Noh Hamlet [PDF]. According to Ueda's website, his tragedography also includes Noh Cleopatra and even Noh Murder in the Cathedral (insert "Who's on First" homage here). Be sure to check out his archives for performance videos.
To return to Noh Hamlet, here's an English backtranslation [PDF] of Noh Hamlet 2004:Horatio: I am Horatio, who served Hamlet, the Prince of Denmark. After his death, following his will, I have been travelling abroad to recount his tragic tale. Even now I deeply regret that, as he felt ill at ease about his heart when he was challenged to a fencing match by Laertes, I could not stop him from accepting it, and he lost his life. So long have I been absent from Denmark that I am now returning home to pay a visit to Hamlet’s as well as Ophelia’s grave. As I have hurried, I have already arrived at Ophelia’s grave. I will sit still and pray for her spirit.