Le Chatelier’s principle when pressure of gases increased with the same stoichiometric coefficient
Your thinking is on the right track. However, what you really need to look out for is number of gas moles.

In order to understand this, think in terms of the equilibrium constant. The equilibrium constant for this reaction is:
$$K_\text{p}=\frac{P_{\text{CO}_2}P_{\text{H}_2}}{P_{\text{H}_2\text{O}}}$$
Remember, since carbon is a solid, changing the volume/pressure is not going to change anything about it, so it is not in the equilibrium constant.

Since we are introducing a supposed change into the system, we have to write its reaction quotient. The reaction quotient, $Q$, is just a way to determine which way the reaction will have to shift in order to return to equilibrium. We write it in pretty much the same way:
$$Q=\frac{P_{\text{CO}_2}P_{\text{H}_2}}{P_{\text{H}_2\text{O}}}$$
Even though it looks the same, remember that we are calculating this after introducing a change. So what we really plug into this equation is the following, where $x$ is the factor by which we increase pressure (suppose that $P_{\text{CO}_2}$, $P_{\text{H}_2}$, and $P_{\text{H}_2\text{O}}$ are the equilibrium pressures):
$$Q=\frac{(P_{\text{CO}_2}\cdot x)(P_{\text{H}_2}\cdot x)}{(P_{\text{H}_2\text{O}}\cdot x)}$$
$$Q=\frac{x^2P_{\text{CO}_2}P_{\text{H}_2}}{xP_{\text{H}_2\text{O}}}$$
Since we are increasing pressure, $x$ is obviously positive. Thus, $Q&gt;K_\text{p}$. 

Due to Le Chatelier's principle, since we introduced a stress into the system, the system will shift away from that stress. $Q$ and $K_\text{p}$ are a good way of mathematically representing this stress. $Q$ is essentially a representation of the system's current state, and $K_\text{p}$ is the representation of the system's ideal state.

So, how do we reach this ideal state? It's simple; we want $Q$ to equal $K_\text{p}$. Obviously this will happen through a change in pressure. Since $Q$ is too big, we need to decrease the numerator in order to make it equal to $K_\text{p}$. The numerator represents the pressure of the products, so the reaction will shift away from the products, using up more products and creating more reactants, until it reaches equilibrium.

Hope that helps.