It's a symmetrical situation. Suppose that A prefers having $1 in his personal luxury budget to having $1 in SIAI, but prefers having $2 in SIAI to having a mere $1 in his personal luxury budget. Suppose that B has the same preferences (regarding his own personal luxury budget, vs SIAI).

Then A and B would each prefer not-donating to donating, but they would each prefer donating-if-their-donation-gets-a-match to not-donating. And so a matching campaign lets them both achieve their preferences.

This is a pretty common situation -- for example, lots of people are unwilling to give large amounts now to save lives in the third world, but would totally be willing to give $1k if this would cause all other first worlders to do so, and would thereby prevent all the cheaply preventable deaths. Matching grants are a smaller version of the same.