That tree looks plenty alive to me. While it is showing plenty of central decay, that dark line next to the rotten interior is compartmentalization: the tree is still fighting off the interior decay. So long as it isn't going to fall on anything expensive as it continues to decay, I wouldn't worry about that.
1. There are many small twigs in the top and peripheral branches.
2. Those branch cuts display lots of color. This is absent in trees that have been dead very long.
3. Vines take a long time to kill off a tree. You wouldn't have that many twigs in the top if the tree has been killed slowly by the choking deficit of sunlight caused by vines.
You can probably determine each live branch right now by looking close at the twigs. Take a good zoomed in picture of any twigs in the tree, then blow them up and look for live leaf buds. Then look at some of the long branches on the ground and compare.
"Buds are tiny leaves, stems and flowers located in a small case at the base of each leaf. Buds are formed during the summer months for the following year. Each spring as the tree comes out of dormancy, the scales fall off and the tree’s leaves, stems and flowers open up and grow."
So if you have buds present on any branch, it almost certainly wasn't killed by any vines. Sometimes branches die as a result of winter-kill, but this isn't as likely for the entire tree, depending on the severity of your winter.
By March, those buds will begin swelling, and in April you will easily tell which parts are alive and doing well.
https://www.naturetalksandwalks.co.uk/what-are-tree-buds/