You have some concatenation issues. As @lrb notes in the comments:
R"+ "WHERE
Would equal RWHERE
which would cause an error.
Also use SQL92 syntax instead of SQL89 with inner join
Instead try:
String query = "SELECT
H.Name as Name,
R.RacesWon as Race
FROM Conditions as C
inner join Races AS R on C.ID = R.ConditionID
inner join Horses AS H on R.HorseID = H.ID";