Is there any publicly available printer at Taiwan Taoyuan International Airport (TPE) that airline passengers can use?
There are a couple businesses within Taiwan Taoyuan International Airport that provide printing / photocopying service.
7-eleven / ibon Kiosk in Terminal 1
You can print out any documents or pictures saved in the memory card, USB, or email the attachment to email@example.com at ibon Kiosk in any 7-ELEVEN stores anytime. All the printing requirements will be easily met. (Options of paper types: A4, A4-160lb, A3 and 4x6)
ibon has independently confirmed the location of their kiosks via their own directory (Chinese only, but I can confirm the address is that of TPE Terminal 1):
hi-life - may or may not be closed
While hi-life provides printing, photocopying and faxing services in their stores. It looks like they do not have a store in TPE anymore (a search within TPE's own website yielded a cached link that leads to nothing upon clicking through).
Post office in Terminal 2
The post office in Terminal 2 (1F) also provides photocopying services, as confirmed on their directory (Chinese only, keyword: 提供影印服務 - providing photocopying services). As of today, the charge is as follow (translation mine):
We only provide photocopies in A4 and A3 format. A4 photocopying cost NTD 2 per page, A3 photocopying cost NTD 4 per page. Double side printing cost double.
B5 paper photocopying is charged at A4 paper rate, B4 paper photocopying is charged at A3 rate.
According to TripAdvisor, the 7-11 convenience store has printers where you can print, scan and fax.
I can't really confirm based on their website (in English, there is a Taiwan website too) because it's not explicit on there but there is a phone number to the terminal where the store is located that you probably can call to be sure.