Short answer, yes, Japan is patriarchal.
For long answer,
Two subcategories need to be made in regards to equality.
1) Legal equality (ie. Are there any laws that favor one sex over the other?)
2) Social equality (ie. Are they treated fairly, and not subjected to preconceived notions).
In America, there is no (1) legal equality, as men have less rights, less opportunities from affirmative actions, etc.
(2) social equality, is hard to say. It depends on the subject.
Does Japan have (1) legal equality? Yes for most parts. Divorce court is more fair for instance, in custody and asset division. They had affirmative actions as part of abenomics. But that failed miserably.
(2) Social equality? Definitely not. At least not in the Western conception of equality (the two sexes are identical in capabilities/affinities)
There is a clear sense of men being different than women in Japan.
Rather than testing for validity of anecdotes, I recommend just reading into Japanese culture. You will get much better sense of what's going on.
I recommend:
1) Abenomics & why it failed
2) Pre-WW2 Era Japanese notion of marriage & duties of a woman.
3) Confucianism in Japan.
4) Yamato Nadeshiko & its prevalence in popular media; characterisation of heroine in media targeting females (esp Morning dramas)
5) Characterisation of the ideal female partner in popular media targeting males.