The meat itself
From my experiencing working with venison, I have come to find out that venison meat is quite "soft" compared to other red meat like beef. You can find a similar kind of "softness" in veal, so it appears the age of the animal, or more specifically, how developed/tough their muscles is related to the texture (and flavor) of the meat.
Here are a few things you can try to improve the texture and flavor:
I believe this is the main culprit for venison. The meat itself is very lean, and when butchering it is common to trim out some of the fat. I recommend to leave a decent amount of fat on the meat, and if you can, keep the harder pieces of fat from the carcass. You can cut those up and add it to the meat before grinding for give it more flavor and firmer texture.
Short of that, or perhaps in addition to that, I can say that by adding beef suet, which is the harder fat of the beef, prepared for processing, really enhances the texture and flavor of ground venison. You should be able to find some at your local independent butcher shop (probably not at the supermarket, but you can ask). Cut it up in small bands and add it to the venison before grinding.
You can try dry-aging the meat. It goes without saying that it has to be done before grinding it. Here is an excerpt from Wikipedia:
The process changes beef by two means. Firstly, moisture is evaporated from the muscle. This creates a greater concentration of beef flavour and taste. Secondly, the beef’s natural enzymes break down the connective tissue in the muscle, which leads to more tender beef.
Do note, even though aging is most often used for beef, that other red meats like bison, venison, moose, etc. are not very dissimilar.
I have noticed that meat which is warmer before grinding tends to make for a more mushy grind. I would recommend to leave your meat in the fridge until immediately before grinding. You can even freeze it slightly (until it has a slight crust) "naked" (unwrapped) for about 30 minutes. This won't improve the flavor, but it will help it retain its shape during processing.
It's most common to process meat through the grinder twice (especially for beef) to give it a more appealing, "silkier" look and texture. If you have been doing that, you may want to try grinding it only once. This is most common for things like pork sausage, and it will leave it with a more "chunky" texture.