Why Capitalize the Word Web?

Because it's a proper noun. It's the shortened form of the name World Wide Web. This is not simply any network or web of computers; it's the network that we connect to for sites like eBay.com, NYTimes.com, Google.com, and so on.

What about compound nouns like "Web site" and "Web protocols?" Just as we capitalize other proper nouns when they appear as part of compound nouns (e.g, "California beaches"), so we should capitalize the word Web in these compound nouns.

Here's another example of the same rule. The World Series isn't just any world-renowned series of games. It's the official name for the annual championship series for professional baseball teams in the U.S. We always capitalize World Series, even when it appears as part of other compound nouns:

World Series
World Series tickets
World Series paraphernalia

Thus:

Web
Web site
Web protocol

The word "Internet," another proper noun, gets the same treatment.

Internet
Internet security
Internet marketing

You might have noticed that the New York Times and other organizations with formal style guides capitalize Web and Internet. Now you know why.