Figured out the problem.
Apparently sp_executesql expects the parameter definition for a table to be of a table type (see this answer for an example: https://stackoverflow.com/a/4264553/21539).
An easier way to solve this problem was to insert the variables names directly into the SQLStatement string as follows:
DECLARE @SQLString NVARCHAR(MAX),
@TableName NVARCHAR(MAX);
SET @TableName = N'[dbo].[MyTable]';
SET @SQLString = N'SELECT * FROM ' + @TableName + ';';
SET @ParamDefinition = N'@_TableName NVARCHAR(max);
EXEC sp_executesql @SQLString;