To understand what this means to the future of software engineering you need to understand two things.
1) APIs are not complex pieces of code (which are and should be subject to copyright). They are very simple descriptions of what a piece of code will do and how to make it do it.
In essence a single API is just one word (the name of the function) and a list of pieces data that should be given to it. it then specifies what will happen and the data that will be returned. An API is not its implementation, it is a high level description of what an implementation should do.
It is equivalent to me copyrighting the sentence
"I am going to the shop, do you want anything?"
When it is combined with the reply
"Yes, some milk."
It is really that simple. Imagine if novelists needed to pay a fee when they used that combination of sentences. Of course they could use "I will go to the shop, do you need me to get something?" Or whatever other variant they need to produce in order to avoid infringing. But suggesting those sidesteps misses the point of copyright. Such small atomic combinations of the basic elements of a language are not significant pieces of work. They are not what copyright laws are designed to protect.
2) Secondly you need to understand the purpose of APIs. They exist so that software programs are easier to write and easier to make communicate with each other. Their purpose is to let one programmer know how to interface with software written by someone else, someone they may have never met, and yet have it function perfectly. The API is a simple contract that says if you want my code to do this, this is how you make it happen.
Another advantage of APIs (well used by software developers everywhere) is that if there are multiple competing programs that do the same thing, then if they all use the same API a software developer can switch between them (almost) effortlessly.
If you are ever frustrated by software not working, Internet sites being unable to perform some task, apps not working on your phone, then I have some bad news for you. If copyrightable APIs become the legal norm, then everything will get much, much worse. Start-up companies and device manufacturers alike will need to protect themselves by ensuring that their APIs are unique and not infringing any one else's copyright. In order to make software that is compatible with something else there will need to be long term financial agreements in place. This will mean that the number of things (devices and programs) that just work together will begin to decrease.
The economic impact is the creation of significant barriers to entry for new technology companies. For the simple reason you cannot create some great new product that will work with products people already have without infringing copyright. Consequently many technical product possibilities will not be explored because of their legal risk. In general copyright on APIs will result in an overall reduction in the pace of innovation.
To you as a consumer it will mean less things will just work out of the box together. It will mean that if you want devices and software to work with each other, then you will need to buy them all from the same vendor. This will be good for the large incumbents in the market place, but for consumers it is very bad.
The sad truth is that if this ruling is upheld you can look forward to less choice and less functionality in your digital world.