Yes, inevitable simultaneous extinction.

The extinction of the dinosaurs (for whatever reason) could have
triggered the demise of mosasaurus and other thermophilac sea life. The
immediate aftermath of dinosaur extinction probably witnessed a major
increase in terrestrial plant biomass in the absence of megaherbivores to
suppress it. An increase in vegetation could have caused a reduction in
atmospheris CO2, absorbed by plants, a reduced greenhouse effect, and cooler
temperatures which, coupled with regression, could have dealt the coup de
grace to thermophilac marine reptiles.

"Could have", but HASN'T. Temperatures remained at Late Cretaceous levels well into the Paleocene, then the methane clathrates in the deep sea dissolved, and temperatures jumped up and remained there well into the Eocene. At the end of the Eocene Antarctica iced over and global temperatures fell, but no sooner. It is a myth that the end of the Cretaceous is connected to any sort of cold climate.

Hey! Why did corals survive? They all need warm water and die in cold one. Or crocodiles?

Since the Triassic, dinosaurs were probably the key element in a warmer
Gaian regime they "invented" and maintained. Suppressing vegetation with
their appetites, dinosaurs kept CO2 levels and global temperatures high,
which facilitated recuperative growth (especially after angiosperms appeared)
and thus maximized the productivity of the land, supporting huge dinosaurian
sizes and populations, even with elevated metabolic rates.

Have a look at climate and herbivore evolution through the Cenozoic and Paleozoic. You won't find a correlation.

If this view is correct, the existence of dinosaurs was essential to the
maintenance of Mesozoic warmth. Sea reptiles were beneficiaries of
dinosaurian dominance and could not survive without them.

All wrong. There were plenty of "sea reptiles" already in the Early Triassic when there were no dinosaurs or anything like them.

A very important point is that the near-simultaneous extinction of
dinosaurs and sea reptiles need not imply a common agency of extinction. The
dinosaur extinction may have caused marine extinctions indirectly, made them
inevitable. Generally, it is assumed that the lack of a common biological
agency of extinction, on land and at sea, implies a common physical agency
e.g. an asteroid. But a biological agency or agencies could have
extinguished the dinosaurs AND, indirectly, the sea creatures, for the latter
may have needed the dinos.

This is still not enough. There weren't just non-neornithean dinosaurs and "sea creatures" among the victims of the K-T mass extinction. How do you (or Dr. Starkov, or whoever) explain the fact that marsupials were decimated? That nearly all birds died out? That 80 % or more of North American plants disappeared within 2 cm under the iridium layer?...

I could argue that the above hypothesis puts the cart before the horse. Let's see it this way: We have an enormous impact crater dated at 64.98 +- 0.05 Ma (and maybe a second one in India + the Seychelles). What happens when a planetoid 10 km across hits the earth?