How many WS2811 LED strips can I control with Arduino?
There are three factors to consider when driving strings of these LEDs from an Arduino:


How much memory the Arduino has - each LED takes at least 3 bytes of RAM (possibly more depending on the library implementation). (An Uno could probably just manage 500 at most)
How long it takes to send the data over the wire - the more LEDs you have in a chain the longer each update takes and the slower your animations run.
How you power such a huge number of LEDs efficiently. You won't just plug them into the 5V pin of the Arduino that's for sure.


Note that the arrangement you link to most likely isn't a single small microcontroller controlling the whole lot. Instead it is much more likely each individual strip has a single controller and those controllers are all networked together (probably through RS-485 or CAN) to a master controller (probably a PC) to send instructions to them all.