My question is, what were these "other open-source software solutions", and what percentage did they contribute? Based only on the information in that article, Linux may have contributed to only a few of those advisories.

Another quote from the article states "Open-source software, commonly used in many versions of Linux, UNIX, and network routing equipment, is now the major source of elevated security vulnerabilities for IT buyers." So, what they are really saying is that all flavors of Linux, Unix, and whatever is on these routers, lumped together, accounts for just over half of the advisories tracked.

What's more, the advisories don't even really pertain to Linux itself, but to other open-source software that is commonly bundled with many Linux distributions. Read the text of the advisories. Only one in 2002 even contains the word "linux", and that is in the name of the worm, not in the software that is vulnerable. The first mention of the OS itself (going backwards from today) is in an advisory issued Nov. 29, 2001. And even in that one the vulnerability is in software that ships with a distro, not the OS itself.