They were generally present beginning in the 1980s. The phone you linked is from the 1960s. The layout with Q and Z was standardized by ITU-T in 1988 https://en.wikipedia.org/wiki/E.161

Earlier in time the letter "O" was also not generally on phone keypads.

According to your link, Q and Z were officially added sometime in the 1990’s, in a later revision. That puts the official change well into my childhood, which explains my out-of-date information; I didn’t put much effort into researching my comment.

the Q & Z assignments shown are typical. That said, few text-based phone numbers include these characters, for the obvious reason.

Depends, I used to have one of these: https://www.geekzone.co.nz/forums.asp?forumid=39&topicid=114...

Though the chart is still wrong according to that, however it (the chart) does match what my Android phone's dialer looks like.

You're correct, which appropriately enough is why you're downvoted. The letters were placed on telephone dials when telephone ‘numbers’ used a mnemonic exchange+digits format¹, so there was no requirement to include the entire alphabet. Advertising mnemonics like the one in the grandparent comment came later, and entering arbitrary text such as names, which actually requires the whole alphabet, much later.

¹ https://en.m.wikipedia.org/wiki/Telephone_exchange_names