It’s really hard to say, there are many factors to consider: oven size and power, the recipe ingredients, pan size and shape, etc. The recipe calls for a 7″ pan, not an 8″ round pan, so I will use the recipe’s specs in calculations. The main question is area, a 7″ pan’s area is about 38.5 square inches (that’s pi times the radius squared), while the area of a 10 x 10 springform pan is 100 square inches, over double that of the 7″ pan. Your cheesecake will actually be thinner than the recipe calls for. A thinner cake will bake faster than a thicker one, but you’re doubling the amount of cake to be baked, which will likely offset that savings somewhat. If I had to make a guess it will likely take about the amount of time in the recipe, although recipes can often be way off in baking times. Other recipes call for baking an hour, not 30 minutes.
The recipe does not say how to check your cake is done, which is not good. Baking times vary according to many factors, and you should always bake for a result using time as a guideline. Most recipes say to bake until it’s a golden brown as your first guideline, given it’s actually a souffle I’d use the touch test, ie push it down with a finger, if it springs back up it’s done.
My advice would be to make this recipe smaller scale before doubling it, make sure you get the ins and outs right before you make it for dinner guests.