Handling multiple "timers" on the board and player mat
There are several ways to implement timers in board games


Tokens. Games like Paper Tales or Pixel Tactics (starting from 2nd set) use addition/removal of tokens from game components to track passage of time. Like this: 



this option works well for cards (or other components you can easily store tokens upon) with relatively small number of simultaneous timers per player (up to 3 in Pixel Tactics and up to 4 in Paper Tales) and small number of ticks.
Dice. Pretty much anywhere you would use token counters, you can substitute them with dice.Example: 

 

In this case instead of
adding/removing tokens you just increment/decrement a die.
Difference here is mostly personal preference, but if you operate
big number of ticks, managing d20 or couple of d6 is much easier and
clearer than pile of tokens.
Time track. Your purposed solution falls into this category, but usually games like Bestiary of Sigillum move track itself rather than items on it. In game it looks like this (on the right): 

 

and this video(russian language) shows how it operates. Basically, each ability has its own token. When ability is used, that token is placed on appropriate number on time track, say, 4. Time track moves one tick each turn and cooldown number for that token changes. When it passes 1, token is returned back and it means that ability is ready for next use.

Another game Tavarua uses similar mechanic, but with segmented
linear track: video example. Both this systems are best for tracking a
lot of timers simultaneously, since they update all of them  with single operation.

I remember an example of time track on which objects are moved rather than track itself. Star Wars: Rebellion uses it as production queue