This is one of Tsukuda Hobby's SF Series games, #9 in that series (the game is numbered HG-009-4000). It bears the subtitle "The Game of Space War in Star Trek" in addition to the less generic "Invasion of Klingon Empire."
This is definitely a strategic game, given the 4-part mounted map showing the United Federation of Planets, the Klingon Empire (or a portion thereof), the Romulan Empire (ditto), and a large amount of space between these. Production is clearly important, as there seem to be many rules sections covering factories.
The game definitely appears to have two sides, the Federation and the Klingons. It gives the appearance of allowing either 2 or 4 players - the map has a line down the middle which would split it reasonably enough for this purpose. Presumably two players split the Federation and the other side has a Klingon and a Romulan player.
The missions of the USS Enterprise are clearly of some importance to the game. The green lines on the map appear to chart these (many of the systems have names familiar from the original TV series), there is a rules section labeled "ST Game Enterprise Mission Chart," and one of the scenarios is called "Missions of Enterplize" (I swear!). Other missions include "la Brandy de Camus" and a campaign game.