Hope I can help, I am a user of XZP since it's launch and also played the above games you mentioned.
I play Starlight Stage, Million Live, Tokimeki Idol, Girlfriend Note, Love Live School Idol Festival.
This phone runs the above games fine before the Oreo update, after update there seem to be some stutters here and there..they are minor though and games should be still playable if you don't mind those issues.
For the touchscreen issue, mine had it but was fixed after sending it to Sony service center and they replaced my touchscreen. From my observation, there seem to be a bad batch floating around.
There is also WiFi issue where it will start dropping for no reason until you restart the device. Not sure how many are affected...but mine is and my phone is still with service center, they keep telling me they are still testing it...
Having said all this...until Sony fix the wifi issue, I do not recommend any SD835 phones from Sony, (eg. XZ Premium, XZ1 and XZ1 Compact)
XZ2 and XZ2 Compact seem to not have the wifi issue so far and it's a very powerful phone as well. However, it seem to have some touchscreen precision problem, you can read more about it here:
/t5/Xperia-XZ2-Compact/XZ2-and-XZ2-Compact-Screen-sensitivity-issues/td-p/1314622
https://forum.xda-developers.com/xperia-xz2/how-to/xz2-touchscreen-sensitivity-issues-t3776021
I do not own the XZ2 yet as I am waiting for XZ2 Premium so can't comment how much it may affect this type of games. Just something to take note.
I now uses the Pixel 2 XL and could recommend it for these games, as the OLED panel had faster response rate and had very low input latency, which is lower than the XZP. It also do not have that strange stutter issue. Some of these games had also recieved patch to support 18:9 aspect ratio.
