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Now that wildfires are such a huge issue everywhere it's a wonder that the word isn't in everyday use.
Such paths, or glades, don't always prevent wildfires, but they sure make the firefighter's job a lot easier.
What are they called?
I've dug up a picture of one; it's from a German page, and the German word for it is "Schneise."
In British English, at least, this is often called a recreation ground. This also seems to fit your description of being in "...bad shape, like missing turf or torn goal nets." as a lot of them are just mown fields, with basic facilities like a couple of goal posts etc.
Colloquially it may be shortened to rec or rec ground in some areas. I think this best reflects the description of somewhere where you would go just to "kick around" like you would on a German Bolzplatz. E.g. "let's go have a kick-about on the rec."
ADDITION:
@Steve – you have swayed me to playing fields, which I get the feeling is a more widely used term in English in general.
noun
1. A road, pedestrian walkway, railroad, bridge, etc., crossing over some barrier, as another road or walkway.www.dictionary.com
Best Answer
Although firebreak is the most common term, you could consider using fireroad, fire line or fuel break as suggested by the Wikipedia article.
Fuel break is defined by Natural Resources Conservation Service as:
A picture of fuel break:
A picture of fire line: