西暦2092年、繁栄を極めた人類は、やがて訪れるであろう落日に向かい、次第に疲弊していくかのようであった。
しかし同年、人類積年の夢であった反重力物質「ネメシス」の発見により、状況は一変したのである。
輸送、交通、建築など、あらゆる分野が飛躍的な進歩を遂げる中、人々が最もその興味を示したのが、ネメシスのある特殊な使用法による時間渡航、「タイムトラベル」の実現であった。
政府は一般でのこの使用法を禁じ、時間渡航禁止法案を定めたのだが、非合法での渡航犯罪が急増。
ついに、「対時間渡航犯罪捜査局」を創設するに至ったのである。
Based on Toritoribeさん's transcript (which I take to be completely correct), I would translate the passage,
"The year 2092. Having flourished to the extreme, humanity has at last headed into their decline, seeming as though they will slowly fall into ruin. However, that same year, mankind's long-standing dream of anti-gravity has been realized in the discovery of the anti-gravity substance 'Nemis(is)', completely reversing the course of events. Every imaginable field is advancing in leaps and bounds, shipping, travel, architecture, and on and on; but among them all, the one people show the most interest in is Nemis(is)'s unique capacity to be used for voyaging across time -- the realization of actual time travel. The government banned civilians from using it in this way with the passage of the Time Travel Prohibition Act, but illegal time travel became widespread. Finally, we reach the establishment of the 'Criminal Time Travel Prevention and Investigation Bureau!'"
(Whether you go with 'NEMIS' (which I suppose is from some official translation?) or 'Nemisis' or whatever is a matter of taste, I think. The derivation from the English is obvious, it's up to you how close you want your name for the substance to resemble the word.)
I'm fairly confident in my understanding of the passage, but of course if I have made any mistakes, I hope nobody will hesitate to point them out so that I can learn from them.
(Actually, I guess, to be completely honest, I'm a -little- fuzzy on 一般... whether it means 'has universally and totally banned time travel' or means 'has banned time travel in ordinary cases (among unauthorized persons)', and at the very end with 至った means 'the government ultimately has reached...', 'the narrative has ultimately reached....' or 'events have ultimately culminated in...'; obviously I translated it with a 'the narrative has ultimately reached...' kind of idea, and probably would do so regardless of the correct meaning of the Japanese, just because it feels better for dramatic reasons as the game goes into the team splash image and dramatic music. But still, knowing the correct interpretation would be for the best!)