I've edited your AHK script a bit and tested it on my system. All keys are working.
The main problem: You sent capital letters to ZP, so ZP did different things than expected. Example: "c" is play/pause, but "C" is Chapter Editor.
Also some key combinations were missing in ZP's key list. You've to configure CTRL+F3/F4 for "Skip 5 seconds backwards/forwards" and SHIFT+F3/F4 for "decrease/increase volume" to make the script work, or change the script to send other keys.
I hope the script works now on your system. FYI: I found no way to send the ALT key to ZP. ZP just ignores it. So, if you want to trigger some ALT+ combination in ZP using the script, you've to change the combination in the key list.
; ^ = CTRL
; ! = ALT
; + = SHIFT
; Info: ControlSend can't send ALT to Zoom Player
; Run Zoom Player
Run,c:\Program Files\Zoom Player\zplayer.exe
;Restart (seek to first frame)
;Next in playlist
;Previous in playlist
;Skip backward 5 secs
;Skip forward 5 secs