Yes; it sure says that alright; but why have you apparently ignored what was said AFTER that?
Jesus gave them a work to do, the work of believing.
The context of Jn 6:27-29 shows:
—that belief itself is a WORK
—one must WORK for everlasting life
So belief is a work one must do to have everlasting life which Christ GIVES for free. Even though everlasting life is a free gift it is NOT an unconditional gift. But comes with conditions and one must WORK to meet the conditions in order to receive the free gift of everlasting life.