Considering all the computers, and video game programmers, and technology and (presumably) money that Japan has -- is [THE ANCIENT DOGOO GIRL] the best [the Japanese] can do with special effects? Or do I just see clips of shows that have really bad special effects?
When you work with a special effects guy, never ask him, "can we do this?" The answer is always "yes." The question is, "can we do this on our schedule and budget."
THE ANCIENT DOGOO GIRL looks like the budget equivalent of XENA: WARRIOR PRINCESS, which, as you may recall, had less than impressive impressive f/x. F/X are getting better all the time, so I won't bitch too much about the BUFFY demon that looked distinctly like a sock puppet. But it's always a question of time and money.
It's also a question of tone. LORD OF THE RINGS has a serious tone, and ambition, and a balrog. Oh, and legions of devoted fans. If you made a balrog that looked anything short of demonic, they would hunt you down and kill you. Whereas if you are making a borderline campy show like XENA, or a comedy, then you can do a lot with smoke and fuller's earth and trivial optical effects.
It's also a question of story. Is your story really about
the magic and effects, e.g. HARRY POTTER? Then they'd better be impressive. If your story is really about the characters' reactions
to magic and effects, you can do a lot offscreen. Or get away with a bit of cheese in your effects.
Note that I'm mixing up movies and TV. Movies have vastly bigger budgets than TV. If you needed to do LORD OF THE RINGS on TV as a series, you'd see the Battle of Minas Tirith mostly from indoors, with lots of sound effects, and people looking out windows and saying "they're coming." And the Nazgûl would be a smoke effect, not a fabric effect. And nowhere would there be wargs or mumaks, because you just can't fake riding a wolf on a TV budget.
So to answer your question: no, that's not the best the Japanese can do. It's probably a low budget SF genre show on the equivalent of SyFy.