At a certain point, showing the traits of a mental health disorder becomes a diagnosis of having a mental health disorder, otherwise nobody would ever receive a diagnosis.
If that threshold is that it is damaging to the relationships around you, then that threshold has undoubtedly been reached with Trump. His White House is full of people that have anonymously expressed concerns over his mental health. This is a sign of strained relationships with those around him.
Additionally, his inflated sense of self-importance and emphasis on personal relationships over the interests of the American people (particularly in areas like foreign policy) are damaging his relationship with government institutions.
He openly rejected the findings of his own national intelligence institutions on Russian interference in the 2016 US election because Vladimir Putin was "extremely strong and powerful in his denial". This damaged his relationship with the intelligence community. 
He has fallen out with and publicly insulted plenty of people who were at one point close to him, including; Steve Bannon, Michael Cohen, Omarosa Manigault, George Papadopoulos, Barbara Res, Tony Schwartz and Rex Tillerson.
Whatever the threshold is for mental illness, Donald Trump's behaviour and inability to maintain relationships clearly indicates that he meets it.