Hi my friend, you are partially correct. Japan has always had a plethora of parties that represented the people in the Imperial Diet. Some examples of the Political Parties that have been a presence in the Diet include the Democratic Party (DPJ), Social Democratic Party (SDP), People's New Party (PNP), New Nippon Party (NNP), New Party Daichi, Liberal Democratic Party (LDP), New Komeito Party (NKP), Japan Renaissance Party (JRP), Japanese Communist Party (JCP), Your Party (YP), Independent Party, etc.
The point of the matter is that the LDP has ruled Japan's Legislative Branch because: 1) It was popular and the population of Japan voted for LDP representatives over others, 2) The alliance system in politics; LDP party members would make alliances with other parties , which then led to majority control of the Diet.
The 2009 victory over the LDP majority alliance was only an example of how party systems operated. But eventually, the LDP won control in 2012 when Abe Shinzo was elected. The beauty of Japanese legislative politics is that those who control the Imperial Diet truly are a representative of the people, since it was the people who elected them and given them the mandate to make responsible policies.
Thanks.