Why are the outputs of these gates tied together in the Apollo Guidance Computer?
RTL logic is open-collector, which allows the wire-OR connection (in this case, more precisely, wire-NOR.) The characteristic of wire-OR is that gates only drive low, so even if more than one is enabled, there is no clash. The gates share a common pullup resistor.
Wire-OR (that is, open-collector or open-drain) is still used. I2C for example is wire-OR. Wire-OR also is used for control signals where multiple devices share the same signal. Example: 'power good' from multiple voltage regulators, or interrupt pins from multiple devices.
The AGC's NOR IC supports a 'fan in' mode, where they connect the gate outputs without connecting the pull-up. In other words, when they connect multiple gates in wire-NOR, they designate only one to have the pull-up resistor, all the others have their pullup resistors left open. This is done to reduce power, and to ensure that the low-drive loading is kept within spec.
Here's the AGC’s NOR IC pinout:

From here: https://djjondent.blogspot.com/2019/07/the-apollo-guidance-computer-nor-gate.html
And here's how it's used in a schematic:

From here: http://klabs.org/history/ech/scd/index.htm
Pull-up vs. non-pull up are shown on the AGC schematics as follows:

pull-up gate: normal NOR (pin 10 connected.)
no-pull-up (fan-in) gate: 'blue nose' shaded output (pin 10 disconnected.)

(Why 'blue nose’? Because... copies from a diazo machine are blue.)