TL;DR: No and Rather Not.
CRT-Screen-Compact-Desktop-Calculators of the 60's
Assuming this is about the Friden EC130/132/1162 series, using a CRT for stack display and a magneto resistive delay line as working storage, like shown here:
Then the answer is a clear:
- Word Processor: NO
- Games: Rather NOT
This is simply due the fact that the delay line memory misses even the tiniest amount of storage to do anything useful. The 5ms line used in the Friden EC130 series (*1), was barely enough to hold 5 registers with 13 decimal places or 65 decimal numbers at whole. Each digit was stored as zero to nine pulses.
Word-Processors - How difficult would it have been to save what was on the delay-line memory onto tape.
Not so much. Still might have cost a few hundred to a thousand 1960 USD (*2) to operate such a tape reliable. But even beside that, it would have taken way more than the available 65 decimal digits of storage to do some useful editing - not to mention that an according display would as well have needed way more storage than the procedural generated decimal digits.
(A simple cable could have connected to printers, or simply take tapes to compatible printers )
A 'simple cable' do what to a 'what'? Sorry, but that part wasn't invented back then. Printers were special to design. Sure, in the early 1960s CDC (and later others) started to build peripherals compatible with (mostly) IBM mainframes, but this as the upper end of market, not anything to come near a calculator type device - in fact, even the interface to handle them might have needed more electronics than the whole Friden 130.
Companies like Centronics, offering vendor independent devices, only came up in the mid 1970s. And no, TTY were not generic.
Video-Games - This would probably involve more circuitry / logic, and of course very few could have afforded one for video games.
Unless this is about some number games, it would have needed a complete different machine. Sure, such could have been designed, but it would not resemble any calculator - after all, why should it.
NOTE - I cannot find how data on Delay-line memory was edited after input, assuming some machines allowed editing, these crt-calculators would probably not have.
It's a RPN stack. A new number could be entered to replace the top entry (bottom line) as often as needed, or the whole stack could be cleared. So, yes, editing was there.
Keep in mind, these were calculators, not computers, and reduced to the minimum needed. Real computers would use drum memory (like the prototype(s) for the EC130 did), or, for extreme high speed, core memory.
Core is what HP used in 1968 for their HP9100, which in turn wasn't a calculator, but already a programmable computer (*3) with 'much' more memory - still not really enough to do serious word processing, not even for a tweet.
Then again, this is already the time when short after full desktop systems like the Datapoint 2200 or Cogar 4 became available, using solid state memory and a CRT.
Long story short, any word processor would (and have) used different technology than the Friden calculators. Likewise any game. It could have been done, but wouldn't have been related.
*1 - The EC132 only differs AFAIR by the way an empty register is filled if values are popped, by copying the TOS value - creating an implied constant memory. The EC1162 again is a cost and size reduced version using integrated circuits.
*2 - The Olivetti MLU 600 tape, used with the 1971 P602 calculator/computer cost ca. 700 USD. So a mid 1960s unit migh have been easy past 1000 USD. Quite a lot considering that a new VW Beatle was USD 1500 in 1960 :))
*3 - Which in turn meant that a court forced them to pay the enormous sum of 900,000 USD to Olivetti for infringing their patents on the Programma 101 series of 1965 - which in fact used delay line memory (with a size of ca. 240 of today's bytes), but had only a printer for output.