Can “sui generis” be placed before the noun?

The example you found is somewhat unusual. In practice, the typical construction is to treat "sui generis" as a postpositional adjective, as your Japanese dictionary suggests. It is possible to treat it as a standard adjective, e.g., "it is a sui generis restaurant" but it looks a bit odd.

The New York Times is quite notorious for doing things like this, calling attention to non-standard vocabulary and phrasing in articles. Also, you're reading a review and NYT reviewers in their art, music, theater, food, and fashion sections frequently push the envelope.

I've seen it both before and after the noun. Here are two examples of its usage I found from a Google search:

"sui generis works like Mary Chestnut's Civil War diary."

"This man, in fact, was sui generis , a true original."

As a note, I would use Latin phrases like this with caution. As you may have experienced, they tend to cause issues with how clearly the point is conveyed. George Orwell's essay Politics and the English Language has an excellent way of critiquing this kind of pretentious word choice:

Foreign words and expressions such as cul de sac, ancien regime, deus ex machina, mutatis mutandis, status quo, gleichschaltung, weltanschauung, are used to give an air of culture and elegance. Except for the useful abbreviations i.e., e.g., and etc., there is no real need for any of the hundreds of foreign phrases now current in the English language. Bad writers, and especially scientific, political, and sociological writers, are nearly always haunted by the notion that Latin or Greek words are grander than Saxon ones.