Hi, running..man. Your mini race report suggests you're aerobically fit, but obviously unused to pacing yourself. The rugby training sounds like a good quality session, one based more on strength and speed than endurance, but you do have to last 80 minutes aswell, so that's there too. If you do take on the running, then you'll aid your endurance on the pitch by taking on long runs, but you don't want to add too much more quality or your training overall (and playing and running) will suffer as you fatigue.
I would do as suggested above and look at getting in a 90 minute and a 60 minute easy run, each once a week and well spread, not together, like Weds and Sun for example. I would also take on a race-pace session to get you to understand it, but I would make this short compared to what full-time runners might do, as you don't want to exhaust yourself. For example, two miles at your average 10k pace, separated by an easy (jogged) mile, and with warmup and cooldown. That might be a forty minute session in total.
The other thing to be aware of is the impact you put on your legs. The majority of rugby training is on grass when outside. Rugby players also tend to be heavier than average with some good muscle bulk. If you do your runs on roads you will be putting a lot of stress on your lower legs. This is another reason why I would keep your running easy - don't push it. You'll get a lot of improvement, including in race pace, out of slow miles. Try to remember to run like a winger not like a prop, even when you're running slowly! 
