This is consistent with the King James and New King James versions. The New King James version states:
“For if you forgive men their trespasses, your heavenly Father will also forgive you."
While this is a minor point, it is a broader translation then simply forgiving people for their offenses against us. It is certainly inclusive, however. To forgive people of any offenses includes those against us.
But what is Jesus trying to communicate here? What is the bigger message?
God unconditionally loves each of us, and perpetually forgives each of us due to that love. There is no need to earn His forgiveness - it is not as if we pay for the privilege of His forgiveness.
Rather Jesus is indicating that it is an automatic process of reception. We won't be able to receive His forgiveness unless we are also forgiving others.
Let's use an example. Let's say that we have a fruit tree and we want to pick its fruit. Will that happen automatically? We can certainly go out to pick the fruit with our basket during fruit season. But if we did not fertilize the tree, it will not give fruit. If we did not otherwise take care of the tree, then it will not give fruit. It will die.
Forgiveness is a similar situation. True forgiveness requires love and compassion. In order to receive love and compassion we must be a receptacle for it. We have the consciousness to be able to receive it.
Let's try another illustration. Let's say that we see a stray animal and see that it is hurt and we want to help the animal. Will we be able to help the animal if it hides and won't let us catch it? Certainly not. We can only help the animal if it trusts us enough to pick it up and help it.
In the same way, by forgiving others for their offenses - against ourselves or otherwise - we can become a receptacle for the forgiveness of the Supreme Being. We come into the realm of love - enabling us to receive his forgiveness.
We have to embrace the act of forgiveness - applying it liberally to others - in order for the Supreme Being's forgiveness will embrace us.
This quality of reciprocation also works with love. Consider this statement of Jesus:
" 'Love the Lord your God with all your heart and with all your soul and with all your mind.' This is the first and greatest commandment. And the second is like it: 'Love your neighbor as yourself.'" (Matt. 22:37-39)
The reason 'Love your neighbor as yourself' is "like it" with respect to " 'Love the Lord your God with all your heart and with all your soul and with all your mind.'" is that without exchanging a loving relationship with the Supreme Being we won't have the ability to truly love others as characterized here.
Again, this is an automatic process. We won't be able to love the Supreme Being without also loving His children. And we won't be able to truly love His children without loving Him.
It would be like having a loving relationship with a woman and yet hating the woman's infant baby. Or loving the baby and hating the woman. How could we hate the baby and love the woman? It is not possible, because the baby is connected to the woman. They are intimately connected.
In the same way, we are each intimately connected with the Supreme Being. It is not as if there is us and then there is God - like we are two opposing forces. The Supreme Being is our Creator and everlasting well-wisher. We are His eternally (whether we appreciate this or not). Thus to portend to love God without loving His children would be a contradiction in itself.
(For a translation of Jesus' statements from the Gospel of Matthew without institutional sectarian influence, see the Gospels of Jesus - translated from the original Greek texts.)