Design of 10th order high pass filter using 2nd order biquads with Matlab and further substitution on to TI AIC3204
Your basic approach seems correct so far.
To implement your 2nd order filters you have to cascade the biquad filters, so that the output of the first feeds into the input of the next and so on.

This is due to the theorem that the overall transfer function $H(z)$ of $n$ cascaded subsystems is the multiplication of the transfer functions of the respective subsystems $H_i(z)$ like this

$$ H(z) = H_1(z) \cdot H_2(z) \cdot \,\, ... \, \cdot H_n(z)$$

So what Matlab gives you, are the coefficients $a_j$ and $b_j$ for the biquad filter transfer functions (called SOS matrix in your result):
$$ H_{biquad}(z) = \frac{b_0 + b_1z^{-1} + b_2 z^{-2}}{1 + a_1z^{-1} + a_2 z^{-2}}$$

To implement it you should use the Direct Form I in time domain - its just the inverse Z-transform of the transfer function above:

$$y[n] = b_0 x[n] + b_1 x[n-1] + b_2x[n-2] - a_1y[n-1]-a_2y[n-2]$$

Now you just have to cascade the filters, so that the output $y[n]$ of the first feeds into the input $x[n]$ of the next biquad and so on.

You may also want to check a similar question asked here: How does cascading biquad sections for higher order filters work?

And also the documentation of the Matlab biquad filter where it tells you how the SOSMatrix and ScaleValues are defined:
Matlab Biquad Documentation