I don't know anything about the educational system in your country. In the US, there would be opportunities to take elective courses outside your major and get some of the qualification needed. But that may not be open to you.
But before you make life changing decisions, there are some things to consider in case you haven't already. First, note that Computer Science is not the same thing as Computer Programming. Programming is just a tool that helps you do other things. No more than accounting is the same thing as business administration.
The online program you suggest might work for you, but first, I suggest a bit of homework. If your college has a department of CS (or a nearby one does), then go there and get a list of the courses that are taken by undergraduates along with their full course descriptions. Look at that and see if it still appeals to you. Some of it might be familiar, but I doubt that anything in your business program will prepare you directly for anything needed in an MS in CS.
So, you will probably wind up with a pretty long path to acceptance in an MS program. Decide if you want to do that but evaluate it fairly in light of other options. Don't waste your life doing one thing when your heart is elsewhere, but be aware of the commitments that you will need to make to change fields.
The online program you named is accredited which means that it is likely to provide valuable education. But also be aware that online education is much harder to be successful at than face-to-face learning. You have much less opportunity to get guidance. It may be (or not) that much less is provided in terms of learning reinforcement (exercises) and feedback (more than grading). Some people can make this work, but it requires more internal drive to do it right.
So, given that it will take you some time to make the switch, think about how best to go about it. If you are fully employed in the business world you need to be able to spend the time to be a success online. If you are a full time student, you need to find a way to support yourself. Time and commitment. Tradeoffs that only you can properly weigh.