No, a tsunami is not just a rapid rise in water. The first wave in the series comes in seemingly as a sudden flowing river, a super tide. But this 'tide' does have great forward velocity as it rushes forward along dry ground, as we have seen in many videos now. Then, after the first wave recedes, there is a "super trough" which sucks the ocean back very far. The next waves which come up after the suck back, over dry seafloor, come as raging walls of water, super waves, which come and come for many minutes as all the water in that miles-long ocean wave pile up and continue forward over the land.
Depending on the offshore islands etc, the waves may refract, double, quadruple etc. That is, in the pictures above we see that the waves are not miles apart. I suspect that in this unique case, the beach is receiving both direct waves and "reflected" waves, coming in more quickly together than if the beach only took the direct waves alone. (See my reply above about the crazy waves hitting the back side of Sri Lanka.)
Each open ocean tsunami wave has a height from trough to crest of a few meters at most, and a period of a mile or more, traveling at 500-600 mph. When reaching shallow water, the front of this wave interacts with the bottom and slows and piles up, going vertical. But the rest of that mile long wave keeps coming and coming, for many minutes, pushing the front of the wave far inland, even in some cases hundreds of feet up hillsides.
I imagine that would demolish any boats/ships in its path...
In post 109 there is a link to the videos. In one of the videos you actually see the sequence of waves coming in.