It is important to understand where you are financially to understand this question. If you have no idea how to create a budget, save money for emergencies, or spend within a plan then you should follow Dave Ramsey until you get to that point. He makes great points on getting out of bad consumer debt. Until you can master this technique obtaining debt to leverage yourself to make more money is dangerous business.
We followed Dave Ramsey and became consumer debt free in early 2014. Then we started a new plan. While I haven't read Rich Dad Poor Dad, I understand that many of his principals are very good as well. I agree that a house can be a liability, especially if you buy more than you need or can afford. However, if you purchase a primary residence that would be equivalent to what you would have rented and overall, it costs you less than if you would have rented, then you are doing well. (This includes, mortgage, repairs, taxes, insurance, maintenance, and opportunity cost).
These guys both appeal to a specific market. They are motivational speakers and their goal is to give concepts that speak to the majority of people. Some of their audience may have no understanding of how to manage their finances, however, some may be very well educated. You must adapt the information that makes sense to your situation.
Once we became consumer debt free (meaning we paid off everything that wasn't tied to an asset), we began leveraging our credit to build up our real estate portfolio.
In your situation, I think the most important question to ask is do you want the security of knowing your house is paid off or do you want to tap into some or all of that equity to start/grow your business. This is all based on your comfort level and risk tolerance. If you are young and have many years until you plan to retire completely then you could stand to have a higher risk tolerance and you may want to pull that money to make some passive income. If you are looking to fully retire in the next 5 to 10 years then you probably want to keep your primary home paid off to keep your living expenses lower. I would definitely not pull that money out unless you have a plan for it to pay for itself and give you a nice income on top of that.
As far as the best way to use the equity, obviously you want to invest it in the possibility that gives you the highest rate of return for your money. The great thing about real estate is that you can get a loan for 70-80% of the value of the property. There are very few investments that you can get that amount of leverage. However, there may be other avenues for you that match your level of risk tolerance and comfort level.
So, in closing, figure out what your goals are, what your level of risk tolerance is, and then look for the situation that will get you there the quickest. Unfortunately there is no black and white set of rules for building wealth and financial freedom. While motivational speaker often have excellent points, they should only be taken as guidance. You should put together all the information you gather into your own "motivational book".