There are multiple ways to increment cell values, but "click[ing] on a cell" is not the best nor easiest way to do so.
Option 1: VBA (only)
Ahh, no. VBA allows the worksheet to take specific actions (such as incrementing a count) when certain events occur, but a Click event is not one of the built-in events for a Worksheet. So I'm going to oversimplify and say "it can't be done". A double-click event (BeforeDoubleClick) is available, however, so if you are willing to double-click instead of click the cells, you might pursue this.
Option 2: VBA and (form) buttons
From the Developer menu, you can place a (form) button somewhere on each category row, and write simple VBA code for each to increment the count for its related row.
To increment a count, you would then click the button. (I named my button "cmdIncrement01"; it is larger than necessary.)
A significant downside to each of the above options is that it involves VBA. To store VBA in a workbook (in a manner where it can be executed), you have to store the workbook as a macro-enabled workbook. With such a workbook, it is easy for anyone who can edit the workbook to insert malware, from just annoying to very damaging.
Option 3: spin controls
From the Developer menu, you can place a spin control somewhere on each category row, and set properties for each and possibly for their related cells with counts. Right click each and select "Format Control…" to specify the linked cell with a count.
To increment a count, you would then click the upper half of a spin control. (In my example, I placed the spin control on the right side of the cell, making it large, and changed the cell alignment to "Right (Indent)" with an Indent Level of 3, but that size and positioning is your choice.)