The vinyl groove is about 25-100 micrometer, and feature sizes on it go down to about 22.5 micrometer [1]. Lasers are extremely cheap today compared to what they were back in the day, and doing laser interferometry to detect features this small is not that difficult. I imagine a hobbyist with the right skill set could hack together a reader for a few hundred bucks at most.
[1] http://www.gzvinyl.com/About-vinyl.aspx