I guess it is gonna be hard to model. Don't know your tool, but as stated by bumboclaat, layering would help.
Reggae drummers nowadays, especially the guy from Seeed, may use trigger on his shells. So we may hear a mix snare.
The sound of his snare sounds like an old ludwig supraphonic (14"x5"), the graal for reggae drummers.

Don't know if you can emulate this kind of tension on a vst, it quickly sounds ridicule. (for instance on bfd or xln drummer)
If the batter skin tension is higher (or lower) than resonance skin,
when hit, the snare will make a "glissando" (?) to meet the resonance skin note.
Thats quick and subtle, but can help forge the sound.
Your modeling soft' doesn't seem to use height of the shell in the process, neither shell material.
What you are looking for here, is metal snare, maybe not bronze, and 5" height.
And of course the drummer is hitting hard, near rimshot (as already stated here)
Replicate this kind of drumming is quite hard ......
I did quit bfd and other vst's to emulate reggae snare drum,
I bought an AT 3030 instead xD
for layering, you may found interesting snare hits on reggae sample cd (and the supraphonic is in bfd if i remember well)

Have fun...


edit : ... and thanks for the video link

 

@Dread_J wow, so many tips and information! I googled for the ludwig and found this audio example. Indeed it is very close:
https://audio1.bonedo.de/d65415c0c4e1ad74ad4fe2f404ecfd53/01 snare mit gussring.mp3

I'll try to find sample sets with this snare, what a beautiful sound! All the info from you guys will help me a lot building the right snare sound!

Thanks ... and you're welcome

 

For those interested: Found a pretty decent recording of that snare here:
http://www.ultimatemetal.com/forum/...mples-includes-ambiece-x-2-hallway-oh.439055/

And sorry for spam posting, I'm just so excited!

 

Sorry, late to the party.
Yes the resonant head is tuned very high.The top is also tuned high but not as high as the resonant.
I can hear the wires.
The snare is not a deep one, probably 14x5,5.
To me it sounds like a brass snare with power hoops.