Islam is the comprehensive religion that includes every part of this life. It left nothing of issues of this life or the hereafter without giving the due illustration for it. A Muslim is the one who accepts Islam as his own religion and perform the other four obligations of Islam. As for the one who does not pray, he is a sinner but we cannot label him a Kafir.
A Muslim is he who believes in the five pillars of Islam. This is the common definition of a Muslim but there are some prophetic tradition that explain the meaning of the ideal Muslim. An example is the hadith that says: A Muslim is the one against whose tongue and hand abuse people are safe. Furthermore, the most important thing that characterize a Muslim from others is to have a good behavior and high manners.
Regarding the point of the one who does not pray and whether he is a kafir or not, Dr. Muzammil H. Siddiqi, former President of the Islamic Society of North America, states:
“According to the belief of Ahl as-Sunnah wa al-Jama`ah, a believer (mu’min) is a person who accepts all that has come in the Qur’an and the authentic Sunnah, and a non-believer (kafir) is he who denies anything that has come in the Qur’an and the authentic Sunnah. Faith requires action, but a person who commits sins and neglects the obligatory duties of Islam will not be called a kafir until he/she denies the validity of Allah’s rules. Thus those Muslims who abandon prayer, Zakah, etc., out of negligence are sinners, and they must repent and correct themselves. In other words, they will not be called kafir unless and until they declare that they do not believe in any of these things and do not consider them necessary and obligatory duties of Islam.”
May Allah guide us to the best way and show us guidance.