(Very) temporary panic and chaos, but not anywhere near civilisation collapse
If the change were not random and affected the top-10% of the global population (the most powerful people on Earth) there would be a remote possibility of the collapse of the modern civilisation. However, when the change is random the collapse is not possible.
The history of the Black Death shows that regardless of the government's competence (some governments were terrible at handling the epidemic), types of response (there were a lot of bizarre types of responses), levels of organisation (some places lost most of their administration due to the epidemic and it took some time to find suitable people to replace them), and cultural differences (many different cultures were affected and they handled the epidemic differently) the civilisation will not collapse despite the high losses. It is estimated that 30% to 60% of the European population died in 1346–1353.
One can argue that the described change is sudden, more frightening, and affects more people simultaneously compared to the Black Death. This is true, but it does not mean that people will lose their minds and start behaving irrationally en masse. Human response to disasters is rarely panic, chaos, looting, or irrational fear. On the contrary, people display altruism, high levels of energy, and surprising levels of self-organisation. People tend to band together and work toward resolving the crisis. This happens in all human societies and all cultures.
The only cause for mass panic in your scenario would be mass media fueling panic. However, since the change is random and 10% of the population is affected all people will have personal experience with the disaster and its consequences. They will have no choice but to stay rational and think about ways to deal with their situation.
You can expect temporary chaos at all levels while people and governments assess the situation and come up with countermeasures. But it will not last long. Even if the central government is incompetent and cannot come up with a coherent plan of action, you will have local governments and organisations stepping in and dealing with problems.
You also need to consider this:
- your newly created monsters are disoriented and disorganised unless their physical change also somehow changed their personalities and made them a part of a hive-mind, therefore, they are no match to humans who have police, army, self-defence forces, paramilitary, and all kinds of organisations with contingency plans and training;
- physical ability to inflict damage is not the same as actual combat prowess, people must be psychologically ready to hurt and kill people in order to use their skills and abilities to the fullest extent (that is why 'good guys with guns subduing bad guys' is nothing more than a myth);
- some percentage of these new monsters will commit suicide due to inability/lack of desire to deal with the consequences of change;
- if new monsters retain their human personalities many of them will join the effort to subdue monsters that lost their sanity, thus, the human response will be stronger.
I would not be surprised if within a year most of the changed beings were hunted down and killed (most likely), locked in research facilities (2nd most likely scenario), or subdued in some other way. Once it is done things return to normal. In ten years no one will care about the mysterious change.
What if the changed people got reinforcements from a parallel dimension?
The outcome will depend on the invading forces and their preparations, plans, strategy, firepower, etc. Anything can happen, including the collapse of human civilisation.
P.S. I strongly disagree with the idea that countries with more guns per capita will weather this crisis better. I believe that countries with better organisation, better contingency plans, stronger governments, and higher public trust in their governments will fare better than countries with highly militarized population but weak and low-competence governments. The proposed change affects 10% of the population and requires an organised response.