The textbook is precisely correct.
The equilibrium constant $K$ which the logarithm is taken of is *dimensionless*, and includes *activities* or *fugacities*, and not concentrations and pressures.
In practice this is achieved by using *standard states* which refer to the pure materials: standard concentration $c^⦵$ and standard pressure $p^⦵$.
One must be very fastidious with units when finding the equilibrium constant.
For example, the reaction 

$$\ce{aA + bB <=> cC + dD}$$

equilibrium constant $K_c$ is exactly

$$K_c = \frac{([\ce{C}]/c^⦵)^c\cdot ([\ce{D}]/c^⦵)^d}{([\ce{A}]/c^⦵)^a\cdot ([\ce{B}]/c^⦵)^b}$$

For pure water in its standard state $c^⦵ = [\ce{H+}] = \pu{1e-7 M}$.
It also correlates with so-called *biological standard state* of $\mathrm{pH} = 7$.
You probably haven't seen it before because many authors use sloppy notations omitting mentioning standard states since they can often be cancelled out.
In this case those cannot be cancelled out, and must be written explicitly.

----------

In fact, your own textbook contains extensive explanation \[1, p. 91\]:

> For chemical reactions the standard state for solutes is defined as $\pu{1 M}$; however, in living cells the concentration of $[\ce{H+}]$ is roughly $10^{-7}~\mathrm M$, much lower than the standard value of $\pu{1 M}$.
It is therefore appropriate to define the reference concentration of $\ce{H+}$ in biochemical reactions relative to the $\ce{H+}$ concentration found in the living state (i.e., $10^{-7}~\mathrm M$), rather than the value $\pu{1 M}$ defined by the chemical standard state.
Recall that when a solute in a dilute solution has a concentration of $\pu{1 M}$, the activity of that solute is unity.
For the biochemical standard state we define the activity of $\ce{H+}$ to be unity when $[\ce{H+}] = 10^{-7}~\mathrm M$.

> [...]

> 2. The mass action expression $Q$ is unitless.
We strip the units from each concentration term in $Q$ by dividing each by its 
proper standard concentration (e.g., $\pu{1 M}$ for all solutes  
except $\ce{H+}$; $10^{-7}~\mathrm M$ for $\ce{H+}$; $\pu{1 bar}$ for gases, etc.).

### Refrences

 1. Appling, D. R.; Anthony-Cahill, S. J.; Mathews, C. K. Biochemistry: Concepts and Connections (Global Edition); *Pearson: Boston*, **2015**. ISBN 978-1-292-11210-7.