No experience with any recirculation pumps on RV but have installed several on home plumbing and it is a pretty basic thing to install.
One basic thought that needs a bit of correction is where the water comes and goes. It will NOT be recirculated from grey to fresh as that is a sure health hazard!
Simple idea is that there is a small pump and a "bypass" to let you turn on the pump, which takes water from the pipe which will become hot and feed it back into a cold pipe, letting that water which might go down the drain, instead go back to the fresh tank.
This has the advantage of letting you use slightly less fresh water, fill the grey tank slightly less soon but with the disadvantage of using more battery power to run the pump!
At home, we have a house that has the hot water heater installed "Texas style" which is basicly outside! Local code requires water heaters to have large vents for letting any gas leak go outside, It also makes your pipes freeze when it gets cold!
But the main problem is that also puts the water heater a long distance from the bathroom, so waiting for hot water does become a problem and it does run a lot of scarce water down the drain!
Enough irritation and waste that I installed a recirculation pump! I added a small Taco pump tied to a digital temp controller that we flip on when ready to shower. The pump take water from the hot side to the cold side until the temperature sensor finds the hot temperature high enough to shut down. I find 100 F to be fine for starting a shower. The little $15 dollar controller keeps the pump from running more than needed and gets me hot water when I want it!
The pump and setup you mention has the little gimmick color thing which is "cool" but not something I would pay extra to get!
Would I do it on an RV? Probably not as we are not prone to worry about running out of fresh, nor filling the grey too soon. We move more often, making those not a big issue.
For each user, I see the question being if the change to holding tank volumes is enough to offset the lost battery power to make it work?
The unit seems to have a gimmick that shows a change in color to let you know when the water has warmed but the install price seems really extreme if one were doing it DIY.
It will vary in each RV due to differences in where the pipes are placed but all it really needs is space near the shower to put a "bypass" between hot and cold pipes for the pump and 12VDC to power it.
We don't get the really good drawings for trailers but I would first look at what it would take to get access to the back of the shower where the pipes go to the faucet. That is often just a thin sheet of plywood which is stapled on. If we can remove that plywood, cut the tubes and place the pump for bypass there is no big issue needing to access the underside. I really would not want the pump added underneath the RV as that tends to be a freeze hazard as well as really difficult.
If one had a really long run for the piping, I might look at it differently but on shorter trailers, not for me. Too much trouble for too little gain, so I might look to other methods like a full water cutoff and navy showers to save the water use.
But that is one reason they make so many different RV! We ALL want something different!