Translation:This path is narrow.
I wouldn't say incorrect, but "way" feels like a slightly unusual choice in this instance.
But 道(みち) can definitely mean "way". It's also in things like 水道(すいどう) "waterway" and 鉄道(てつどう) "railway".
I've learned 細い through the 通りゃんせ children's song used to describe a narrow path.
Perhaps せまい is for narrow and ほそい in terms of a path is more like a winding foot path? Or ほそい could just be more poetic?
せまい is mainly used as a description of places (e.g. a room, a field) or one's views (e.g. to be "narrow-minded").
ほそい is most often used to describe things that use the counter 本（ほん）; i.e. cylindrical objects.
細道（ほそみち）also refers to a narrow path or lane, but differs from the above in the sense that it's a single noun rather than an adjective + noun.