AFAIK hardware 'compatibility' on linux boils down to whether or not a device is supported by the linux kernel. If it is, then this 'support' can come in one of two forms:
1. the 'device driver' has been compiled directly into the kernel itself; or
2. the 'device driver' has been compiled as a kernel module.
For a general purpose distro like Puppy, it is highly UNlikely that device drivers are compiled into the kernel and it is highly LIKELY you will need to install the kernel module (aka 'device driver') appropriate to your video capture card.
The act of installing a kernel module is very easy. Simply open a terminal and type:
modprobe <name of the kernel driver>
In practice, however, it can be a bit more involved.
You can only do the above once (a) you have the kernel driver on your system, and (b) it is in binary form. This is the same for any driver whether it be for your sound card, your ethernet card, your wireless card, etc.
Kernel modules are located in the directories and subdirectories under /lib/modules/<uname -r> where '<uname -r>' is the kernel number which you can find out by typing:
In a terminal. Puppy 2.13 uses the 184.108.40.206 kernel, so the directory would be /lib/modules/220.127.116.11 but you will have to look at the subdirectories as well (my memory fails me). Kernel modules have '.ko' as the last 3 letters in their name.
This, of course, only helps you if you know the name of the kernel module you're looking for. I'm afraid I can't help you with that. Hopefully someone else can help you.
btw, you didn't mention the source of the digital video you wanted to capture - DVB (digital TV), video camera, or both?