Yes. Non-muslims are committing haram by not believing in Islam and by not practicing its constituents such as by not praying, and by not giving zakat etc. There are verses in the Quran which condemn them for it:
ما سلككم في سقر قالوا لم نك من المصلين ولم نك نطعم المسكين وكنا نخوض مع الخائضين وكنا نكذب بيوم الدين
"What has caused you to enter Hell?". They will say: "We were not of those who used to offer the Salât (prayers). Nor did we used to feed the poor. And we used to enter into vain discourse with those who engaged [in it]. And we used to belie the Day of Recompense.
— Quran 74:42-46
وويل للمشركين الذين لا يؤتون الزكاة وهم بالآخرة هم كافرون
And woe to those who associate others with Allah - Those who do not give zakah, and in the Hereafter they are disbelievers.
— Quran 41:6-7
فلا صدق ولا صلى ولكن كذب وتولى
And the disbeliever had not believed, nor had he prayed. But [instead], he denied and turned away
— Quran 75:31-32
The implication in the eyes of Allah is that they are punished in this world, the grave, and in the hereafter they are in Hell. And the implication in relation to the Muslims is that they will be treated as kuffar in all matters of law - the details of which are too extensive to cover here.