Rewards result from the Way of Life
The phrase is not so surprising if one considers the tone of Didache from the beginning. It juxtaposes two ways: the Way of Life and Way of Death, promising blessedness and happiness as rewards for those who follow the former, and implying punishments for the latter. There follows a long list of both positive and negative Christian commandments, many related to OT equivalents. Chapter 4 cautions:
Do not in any way forsake the commandments of the Lord; but keep what
you have received, neither adding thereto nor taking away therefrom... This is the way of life.
The implication is clear: those follow the Lord's commandments are rewarded. As Jesus said in Matthew 5:6 -
“Blessed are those who hunger and thirst for righteousness, for they will be filled. Those who habitually violate Jesus' commands never know the blessedness that results from consistent moral behavior.
Why this was important
The OP asks why this was important. The answer probably lies in the attitude that Paul warns against in 1 Cor. 6, where certain members of the church had misunderstood his teaching to imply that, because Christians were not saved by obedience to the Law, they could simply ignore its dictates:
“All things are permitted for me,” but not all things are
beneficial... The body is meant not for sexual immorality but for the
Lord and the Lord for the body... Shun sexual immorality!... Do you
not know that your body is a temple of the Holy Spirit within you,
which you have from God, and that you are not your own? For you
were bought with a price; therefore glorify God in your body. (6-20)
Early Christians would understand the moral teaching of Didache in a straightforward manner. Those who follow Jesus' moral commands are rewarded with with blessings and happiness. These follow the Way of Life. Their opposites are "persecutors of the good, hating truth, loving a lie, not knowing a reward for righteousness, not cleaving to good nor to righteous judgment, watching not for that which is good, but for that which is evil." These follow the Way of Death, and do not know the rewards that come from the Way of Life. The teaching was important as a warning against the antinomianism that resulted from misunderstanding the Pauline doctrine of freedom from the Law.
Note: Those Christians who accepted Paul's teachings would understand this section of Didache as an encouragement to manifest the fruits of the Spirit. (Galatians 5:22-23) However some commentators hold that Didache is a Jewish-Christian document that did not accept the Pauline doctrine of salvation by faith alone.