I’ve never heard of this problem before, which probably means that it’s mostly of interest to nuclear physicists, which is not my field of atomic physics. (We just care about stuff orbiting around the nucleus 
) Reading the news and Wikipedia articles, there doesn’t seem to be any obvious new physics beyond the SM implications of this result.
Yes, this is big news; the EMC effect is an important longstanding problem in nuclear physics.
Here is the gist of the problem:
- Protons and neutrons are composed of smaller particles - the most prominent of which are quarks. Imagine a proton as a spherical bag, and inside that bag are spherical marbles (quarks).
- Suppose this bag is coming straight at you at incredible speed (this is the situation in particle colliders, where particles are accelerated to incredible speeds).
- The momentum of the bag can be obtained by adding together the momenta of each marbles (for this simple picture, the bag itself is massless). For example, the first marble contains 10% of the momentum of the entire bag, the second marble contains 60% of the momentum, and so on.
- Through nuclear physics experiments, we know the probability of a given marble to possess X percent of the momentum of the entire bag. This is the parton distribution function.
- However, it turns out that this distribution is different if you measure it for a free proton or a proton that is part of the nucleus of an atom (which is a collection of many protons and neutrons).
So to reiterate: the momenta distribution of marbles in an atomic bag that is racing towards you is different whether the bag is alone (free protons) or part of a collection of bags travelling together (an atomic nucleus).
Ah you say, but this is because in the case of an atomic nucleus, there is the nuclear force that keeps the collection of protons and neutrons sticking to each other! Surely this extra force messes with the distribution of momenta of the constituent protons. Nope: the energy associated with the nuclear force is miniscule compared to the energy associated with the momenta of the proton.
The actual cause of the EMC effect is unknown for now. There are many competing theories for the EMC effect, and this paper presents experimental evidence for one of them.