Why do they keep series resistor with each open drain output during Wired OR logic?
Yes, it is a wired OR logic &quot;gate&quot;. The 10 k resistors R1-R4 protect the output from being short connected to ground when a button is pressed. They form voltage dividers with R5 but their resistance is negligible relative to R5 (only 1/10).
At first glance, this seems pointless, but probably the output is connected to a microcontroller port pin that can be programmed as both input and output. If it is accidentally programmed as an output, when a button is pressed, it will be short-circuited to the ground.

In the explanation above, I assumed these were buttons. If they are open drains, the reason is similar but now they can be damaged.
There is always a risk of an open drain (collector) being damaged. Many years ago, a friend of mine (designer) told me, &quot;If you leave a collector open, there will always be a fool to connect it to the supply voltage.&quot;