Is this sponge cake recipe correct?
Different types of cakes are recognizable by their ratios. Recognizing the ratio of your recipe is very hard, because it is given in nonstandard volumetric measurements. In fact, the use of "flour" (without differentiation of the type) together with cornstarch, and the formulation "heaped tablespoon" suggests that this is a continental European recipe, where tablespoons are not a normed measure from a standardized measuring system. Your relatives probably used whichever spoon they had in the cupboard to measure the flour and sugar. 

Still, unless they had some giant sized spoons, the cake is quite heavy on the eggs. A standardish sponge would be around 1:1 eggs to flour by weight, while my conversions give me less than 200 g flour and about 500 g egg for even generously heaped tablespoons. Home laid eggs would have been smaller, but not half of today's ones. Also, the lack of fat is suspicious. In comparison to standard Western cake recipe categories, it is closest to a genoise. The second best match is angel food cake, but the use of baking powder and the high egg ratio is quite off for it. 

The unusual thing is that it uses baking powder, since both a traditional genoise and a traditional angel food cake are purely egg leavened. It is likely to be a home baker's addition to a more traditional recipe, either because of a misunderstanding (some people don't realize that you can make cakes without chemical leaveners) or because they had difficulty to get it rise without it and added it to get a rise. 

If you are asking whether you should try it: you can, or you can try a different genoise recipe from somewhere else. The advantage of using a modern source is the reproducibility and better testing - when you heap your own spoons, you will likely end up using a very different amount of flour than whatever your relative used. Also, if you have never made a genoise before, it's a more difficult recipe than typical sponges. It is very sensitive to the proper ratio, proper duration of mixing, and proper baking time and temperature, and people usually need a few practice tries until they master it. It's not rocket science, more like throwing darts - invest your time and it's learnable, just don't expect perfect results the first time round. 

The learning curve is another reason why I would suggest looking around for a different source for a genoise recipe. If you make this one and it goes well, great. If it doesn't, you won't be able to troubleshoot it well until you have learned how it's supposed to work, which is best learned with a tested recipe with good instructions, not a grandparent's notes to a process she knew by heart. 

Still, the recipe does have a chance of working, it's not a totally unusual one. If you really insist, you can try making it. Just set your expectations properly and don't be disappointed if it isn't an instant success.