I just got access to Chrome 38 on a high DPI screen and it shows the same behavior.
DPI :
chrome.browserAction.setIcon({
path: {
19: "img/logo-off.png",
38: "img/logo-off-hidpi.png"
},
tabId: tab.id
});
Chrome DPI. 19x19 38x38.
( 2016):
Chrome, , Material Design , 16x16 (32x32 HiDPI). , ( Linux, ).