Search for rows with coordinates within a Polyline
When Google says Polyline they're referring specifically to the Encoded Polyline Algorithm Format. That's a rendering format though. Essentially, you're rendering a point (with longitude, and latitude) as an ASCII string for easy API-transfer. That's not useful to you.

In GIS terms, what you need to do is take the Polyline from Google and construct a GIS LINESTRING from it. A GIS LINESTRING is a series of sequential points. For completeness in parlance, a line segment is a LINESTRING between just two points. A LINESTRING includes one or more line segements.

How do you get the Polyline to LINESTRING? There are many ways. For PostgreSQL with PostGIS that's easy because you have ST_LineFromEncodedPolyline which will do it. In MySQL you'll either have to do this in the app, in your case PHP, or write a very complex function (like ST_LineFromEncodedPolyline in PostGIS) to do it.

Personalized advice: in your case I would convert from PolyLine to WKB in PHP and then bring it into the database with ST_GeomFromWKB

Either way, after you have the LINESTRING you'll have to 


Buffer the LINESTRING to create a POLYGON with ST_Buffer
Use MBRCoveredBy(linestring|polygon, pt)


Then in the end, it'll look something like this,

SELECT MBRCoveredBy(
  ST_Buffer( ST_GeomFromWKB( ? ) , DISTANCE_IN_METERS ),
  t.pt
)
FROM TABLE as t;


Where ? is the WKB output from PHP.