See this bug on chromium. Essentially it boils down to security settings that are not available unless the Mac app (Chrome, in this case) is released through the Mac App Store.
Note that due to the way Handoff is implemented in Chrome/Mac, the current tab from Chrome/Mac can be opened in Safari/iOS. When you are in Handoff range and have an open tab in Chrome/Mac, you should see the Safari icon in the lower-left corner on the iOS lock screen. Swipe up on it, enter your PIN or passcode if applicable, and it should open the page in Safari. Alternatively, if the phone is already unlocked, double-tap the Home button to open the Application Switcher, and swipe all the way to the left.
I added a suggestion to the above-referenced bug that they implement an "Open in Chrome" app extension for Chrome/iOS that would allow quickly opening the current Safari/iOS page in Chrome/iOS.