Actually, that's a generic definition of the term but it will still do. Let's consider: 1. "A breach of allegiance to one's government,"
Did Davis breach his allegiance to the United States government, which also using a legal definition would entail a violation of some duty on his part at a time when his allegiance was in binding existence? No. He did not. In fact he very publicly ended his allegiance in a Senate speech and went his separate way from the previous government before engaging in any operation of the war.
2. "usually committed through levying war against such government or by giving aid or comfort to the enemy."
Did Davis levy war? Well, yes he did. But he did so as a belligerant power (the confederate government) against another belligerant power (the union government) under the laws of war, not of treason. If one were to extend the definition of treason to include ANY act of war against the United States - a proposition that would be necessary for your assertion to stick - by a similar token Japan would be guilty of treason against us in 1941, Germany in 1918, Spain in 1898, Britain in 1812 and so forth, rather than being belligerant powers.
3. "The offense of attempting by overt acts to overthrow the government of the state to which the offender owes allegiance"
Did Davis attempt to overthrow the government of the United States? No. He did not, nor did he owe any further allegiance to that government, having publicly ended it some months prior. The confederacy sought but one thing - it's independence - and no more wanted to gain control over the northern states than the colonies wanted to control London in 1776.
4. "or of betraying the state into the hands of a foreign power."
Did Davis betray the United States into the hands of a foreign power? No. He did not, thus no treason occurred.
And that is meaningless.
If Arnold had resigned his commission before he went to the British he would still be a traitor.
Stop double-talking.
The treason may have been legimate, but it is still treason.