A metaphor (similar to drive, groove, etc.) referring to the agility of the San Franciscan business scene in the late 1990s ("New Economy")

Vibe is short for vibration and here it refers to the excitement and flurry of entrepreneurial activity in San Francisco in the 1990s. The law firm evidently attracted clients which were part of this entrepreneurial wave. (Presumably, though without seeing your context, I can't sure -- the firm advised startups, possibly small companies and tech companies especially, and worked with venture capitalists.). Alternatively, perhaps it had key personnel who were involved with these companies in ways other than providing them with legal services -- say, as investors, board members or spokespersons. Therefore, other businesses -- which may not have been entrepreneurs/entrepreneurial themselves but wanted to be associated with the city's/regional entrepreneurial activity -- retained the services of the firm.

See this definition on the Web:
vibe: a distinctive emotional atmosphere; sensed intuitively; "it gave me a nostalgic vibe"; "that man gives off bad vibes"
http://wordnet.princeton.edu/perl/webwn

Note that it's possible to get either "bad vibes" or "good vibes" from a situation. The connotation here is definitely good.