tl, dr: the LEDs, if a type with Vf around 2V (red, yellow), will drag the Voh below an acceptable level, causing the circuit to malfunction (or at least be out of LSTTL spec.) The LEDs should be buffered.
The more Ben Eater stuff I see, the less I like. This is no exception.
Let's dig in a bit. First, what does an LSTTL output look like? This:
From here: https://www.ti.com/lit/ds/symlink/sn54ls08.pdf
See those two transistors at the right? They are a totem pole NPN pair, with a 120 ohm resistor in series with Vcc.
So what will happen to that 'LS173 output type with Ben's LED glommed onto it, so rudely without even a courtesy of a current limiting resistor? When the output is high, the LED will clamp to its forward drop voltage (Vf), with the current limited by the 120 ohm series resistor.
This might work if Ben choose a green, blue or white LED with Vf > 3V. Red or yellow? Nope, those usually have Vf around 2V or less, so Voh won't be high enough (needs to be at least 2.4V to meet TTL Voh spec.)
Example LED Vf vs. current (from here):
With this LED, you can see that even at only 3mA, the output isn't making it to 2V, the minimum Vih spec, let alone the 2.4V Voh required for margin.
The fun part is, this V-I curve varies not only by LED color, but even within the same color from the same vendor, by the specific part. And, this can vary from LED to LED even within the same type.
It's literally luck o' the draw whether that red LED will let the '245 see an adequate Vih to work.
Flaky at best, non-functional at worst.