what makes a DMR...a DMR?
I'd say, the definition is just as blurry as the definition for a "sniper rifle". For any specific army, whatever they put in the hands of a designated marksman as an issued rifle is going to be their DMR.
If you are looking for a more general definition or a collection of criteria that a typical DMR would have to meet, then the first question to ask would probably be: What's a designated marksman?
A coarse answer would be, a soldier who is commonly attached to standard infantry (in contrast to a scout/sniper team, which would rather be deployed in a more independent way), and who is supposed to be able to engage targets at a longer range than standard infantry (however typically still more limited in range than a sniper team).
Standard infantry would typically engage targets at ranges up to 300m, designated marksmen should be able to reach out to ~600-800m.
The DMR would ideally be a tool that is suitable for the job, so based on that,
- it would probably be a scoped rifle (while standard infantry may use iron sights, non-magnifying red dot sights, etc.)
- it may be a larger caliber than the standard infantry's rifle (e.g., 7.62 instead of 5.56 or 5.45) for better long range performance
- it would typically be a semi-auto (while snipers often use bolt-action rifles, and standard infantry often use select-fire rifles)
- it would commonly be smaller and lighter than many sniper rifles, because designated marksmen may move at a faster pace, along with other infantry
- it would ideally be accurate enough to be useful at longer ranges, so I'd say, at least < 2 MOA or better
- obviously, any DMR had better be somewhat suitable as a military rifle; that would include: robust design, standard caliber (not something exotic), standard rails, etc.
But does it mean a semi auto, bolt action, select fire?
I would say it does not necessarily mean anything. I don't think there is any generally accepted strict definition of how a DMR has to be designed.
Labeling a rifle a DMR basically just means that some army (or some manufacturer, whoever puts the label on it) thinks that this specific rifle is suitable for use by designated marksmen.
It's the same with "sniper rifles". Snipers in WWII used rifles that probably would not be labeled a "sniper rifle" by most manufacturers today, but obviously they were the right tool for the job back then, so from a historical point of view, they are "sniper rifles". What makes a rifle a "sniper rifle" today is typically the fact that someone thinks it would be an ideal tool for a sniper. An army may select some specific rifle as the standard issue sniper rifle, thereby making it a sniper rifle. A gun manufacturer may call it a sniper rifle, because that's the purpose they had in mind when they designed it. A police unit may call it a sniper rifle because it's the rifle that their SWAT marksmen use.
Regarding the blurry line between sniper rifles and DMRs, the Dragunov SVD is one example. It is sometimes labeled a sniper rifle and sometimes labeled a DMR, by various people, for various reasons, including how russian sniper are deployed and the design of the gun itself.
Not really, just adding my $0.02