But if an atheist is doing something, He is purely doing it for the love of people, Isn't it?
There is an debate in philosophy (Psychological egoism) that all humans are inherently selfish beings. All of their behavior is in their self-interest and motivated by their instinct of self-preservation. Some of them may be deluded into believing that they are being altruistic, however subconsciously even their actions are motivated by expectation of reward and fear of punishment.
An atheist may not expect reward from God in the hereafter, but he may anticipate some form of reward in this life from other people. Suppose that he seemingly selflessly gives charity to a homeless beggar. However rewards that he could actually be craving are:
Reciprocity. He might perceive some direct or indirect benefit from his act at a later time. The beggar himself may be in a position to help in a different situation; or the aim might be to propagate the value of generosity in society which could at some point be useful to him and his children etc. Perhaps it is this expectation of recompense that the atheist is seeking?
Gratitude, praise and recognition by the people. The person he helps will be thankful to him, the society will appreciate and glorify him. All of these will make the atheist feel good about himself. Perhaps if it is this feeling of pleasure - the high caused by release of hormones - that the atheist is seeking?
So, is his act really for the love of people, care, humanity? Or does he have something to gain from it? If he has something to gain or lose, then it is suspect whether his motivation is truly selfless. And his claim of having some sort of moral superiority over a believer is debatable.
Can we do good deeds saying god, god you don't have to count this, this thing I am doing only for the love of people, care, humanity, etc,..?
As Muslim you should do good deeds for pleasure of Allah and hoping for reward from Him.
❝ And whoever desires the reward of this world - We will give him thereof; and whoever desires the reward of the Hereafter - We will give him thereof. And we will reward the grateful. ❞ - Aale Imran 145
❝ Those who enjoin charity or that which is right or conciliation between people. And whoever does that seeking means to the approval of Allah - then We are going to give him a great reward. ❞ - An-Nisa 114
Can you afford to relinquish your reward and tell God "you don't have to count this, this thing I am doing only for the love of people" you may find that out when the time of accounting comes.
❝ That Day shall a man flee from his brother,
And from his mother and his father,
And from his wife and his children.
Every man, that Day, will have enough to make him careless of others. ❞ - Abasa 34 to 37