I have the exact same problem as the OP. I have the same Lenovo Yoga 720-15IKB. Touchscreen does not work with my fingers but the pen that came with it still works.
I've read plenty of these posts but none mention seeing something like this .
Last night I had a few browsers open and was casting a video to my TV when the laptop screen started zooming in and out as if I was pinching with 2 fingers. My fingers wouldn't resize the browsers to fix it so I had to use Ctrl+0. It did this a few times so I just shut the laptop down and used my phone. Today when I turned it on I found it was completely unresponsive to my fingers. I only tried my pen after seeing a few other people say the pen works when fingers don't.
I'm running Win Pro 1809 Build 17763.379. After the stuff around with the 1809 upgrade deleting files last year I've got my Semi-annual (Targeted) feature update set to 45 days in preparation for such madness to occur again. I don't think my version matters as there are people all over multiple forums with different versions and the same problem.
Looks like there was a ton of problems with the touchscreen on this laptop around the end of 2017 when Windows updated from 170x to 1803. Lots of people said Lenovo informed them they were waiting on a patch from Microsoft. My touchscreen has worked pretty much fine from when I bought the laptop in Oct 2017 till last night.
I've tried Windows Update, disable/enable and uninstall/restart and update the HID-compliant touch screen.
I downloaded and ran the Lenovo Diagnostics program and tested the touchscreen. It failed all tests as it was asking me to touch different areas in different ways and it wouldn't detect any touch from my fingers.
TouchGate is already set to 1.
Some people suggested going into the BIOS to see if it works in there but mine looks like a legacy BIOS and not a UEFI so not touch or mouse or trackpad worked in there. Just normal arrow keys, Enter, Esc, etc.
I didn't install anything and no hardware changes and nothing plugged into any ports other than the charger
The only updates yesterday (14th April 19) was Firefox and Microsoft Office. 8 Days before that was Dropbox and Chrome.
The last Windows updates (apart from virus definitions) was on the 21st March 2019 and was KB4489899 and a Flash player update.
I have all the latest drivers from Lenovo's support page for this laptop (although saying that, they don't actually list one for the touchscreen). Of course some of them are a bit older than the most up to date generic drivers but I'm reluctant to install generic ones yet. Using the open source driver updater called Snappy Driver Installer Origin I downloaded a Wacom driver and tried that. It just added a new entry in Device Manager under HID called 'Wacom Device' and oddly kept the original dodgy generic 'HID-compliant pen' Windows driver from 2006 (can't believe Win 10 still uses these everywhere!). It also added a Wacom control panel with a few options but didn't let my fingers work. Upon restart, the pen stopped working too and I found the Wacom applet in Control Panel gone and the Start Menu link to a file called 'ISD_ControlPanel.exe' that had disappeared. I uninstalled the Wacom program and very weirdly after it finished, the missing file and control panel were back! So weird. So the pen seems to work fine with either the Wacom driver installed or not. Anyway, this driver package made no difference to my fingers working on the touchscreen.
I did some more Googling before posting this and found 6 entries of the same problem on Reddit without looking too hard. Seems it's quite widespread and no one seems to have a good solution other than that time the Microsoft update killed it. Apart from that, it seems likely I'll have to send it in for repair.
Unless anyone has any new ideas?