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A working two-integrator oscillator - without some additional means to add phase lag - requires real opamps.
The discussion shows also a disadvantage of the Falstad animations - not to mention the exact device parameters. You can only conclude by implication that it uses ideal OPs (with additional voltage limiting). A small rounding error is apparently responsible for a slowly decreasing oscillation magnitude in the equal resistor case.
In so far I agree to your general reservations in post #14.