I concur with Wildcat6305 that it would be clearer for YG’s Victory Objectives to distinguish between the Allied and Axis objectives pertaining to the Burma Road, because they’re different objectives. The Allied objective is to control the Burma Road, by holding all of it; the Axis objective is to cut off (or block or interdict or shut down) the Burma Road, by holding one or more of the territories it traverses.
The Allies are the only ones who get any economic benefit from controlling the Burma Road, and in order to do so they need to control all of it. As the OOB rules say, “When all of the territories this road passes through are controlled by the Allies during China’s Collect Income phase, China receives a bonus income of 6 IPCs per turn” and “Allied powers must control India, Burma, Yunnan, and Szechwan for this to occur.”
It’s clear from the OOB rules that the Axis powers only have to occupy one of those territories to knock the Burma Road out of action, and thus that they don’t need to “control” all of it to achieve their aim of denying income to China. Saying that the Axis needs to “Axis control all territories connecting the Burma Road” contradicts what the OOB rules say. Moreover, the Axis gains no income from the Burma Road even if it “controls” all of it, so from this perspective too it’s potentially misleading to give the Axis a goal of “controlling” the Burma Road.