Starbuck's CEO Schultz is a smart cookie. He realizes while raising the minimum wage will ameliorate the problem, it is ultimately not a solution. Wages for low-skill jobs are low because of simple supply/demand economics. Too many unskilled workers + not enough jobs for them = low wages for them.
Schultz recognizes that the ultimate solution is to change this supply/demand balance. Technological progress means low-skilled jobs are disappearing, so the only avenue available is to reduce the number of unskilled workers. We need to educate them so that they are no longer unskilled or low-skilled.
So the whole point of this program is to educate people in a medium-skill or high-skill job. That way they are able to get a better, higher-paying job, removing themselves from the supply of unskilled workers, thus helping to naturally increase wages for unskilled workers.
The point of this program is not to let you get a degree in something you think is "fun" or "always wanted to do" with zero regard for its applicability or usefulness to society (the mistake most kids make when their parents are paying for their education). You're supposed to study so you can get a job which takes some skill, but is readily available and useful to society, and hopefully you enjoy doing.
You see, while raising the minimum wage alters the income distribution, it is a zero-sum proposition (possibly even negative-sum, as it eliminates some low-end jobs). It does not increase the net productivity of the population, so it is merely dividing the pie a different way. OTOH, educating people for a higher-skill job increases their productivity - it makes the pie bigger, and is thus the preferable solution.