Like all memes, these offer no explanation, just a bald claim that these four things are, somehow, evidence against the Earth being a globe. Not even evidence of a flat Earth, mind you, but just evidence that the Earth is not a globe.
How? You may well ask. Fortunately, or unfortunately as the case may be, I have been around this scene long enough to know what the maker of this meme is going on about. And to know that whoever it is is not only wrong, but actually leading us to evidence that the Earth is, indeed, a globe. Let's take these one at a time:
The conceit here is that periscopes would be useless on a curved Earth because the submariner using the scope would be limited by the horizon. And, in fact, that is the case. Which is why periscope masts are generally far taller than the one in the picture, to extend the horizon, something that is only necessary on a curved Earth.
Further, the fact that the Earth is curved by a, for all practical purposes, fixed amount was used by periscope operators, in the days before sonar, to target ships for attack. The distance to the horizon was calculated using the height of the mast above the water, something that can only be true on a curved Earth. Strike one.
All kinds of wild claims are made for lighthouses by flat-Earthers. Eric Dubay, in his 200 Proofs the Earth Is Not a Spinning Ball, states that the Cape L’Agulhas lighthouse in South Africa can be seen from 50 miles away. Other flat-Earthers claim that lighthouses can be seen from hundreds of miles away. No sources are cited for these claims, and articles by real sailors state that the maximum distance any lighthouse can be seen, under the best of conditions, is a little over 20 miles.
But the telling question is: why are lighthouses so tall? In a flat world, lighthouses could be only tall enough to rise above the waves, which would save a lot of money on their construction. But lighthouses are made tall to be seen from greater distances. which is only necessary on a curved Earth. Strike two.
The notion that gyroscopes don't "work" on a globe Earth is, on its face, ludicrous. Whether the Earth is flat, round, or octahedral, a gyroscope will do what a gyroscope does. What does a gyroscope do? It maintains a fixed position in space, independent of gravity, absent any intervening force.
So what's the big deal? Gyroscopes are used in navigation, in artificial horizons. The flat-Earthers claim that the artificial horizon would roll back as the plane flies, because the plane would have to curve around the Earth while the gyroscope maintains its fixed position. And they are right about that. Which is why artificial horizons have a device to compensate for gravity built into them; they are not merely gyroscopes. If you're curious, look up "pendulous vanes."
Flat-Earthers have made YouTube videos about gyroscopes, filming them in time-lapse and noting that they do not move. All of these are flawed by several factors, not the least of which is the use of a toy gyroscope that is subject to a great deal of friction. They prove nothing except the experimenter's inability to design a controlled experiment. Strike three. Flat-Earthers are already out, but they still feel the need to come back to bat for a good chance at getting beaned with the ball, which leads us to:
I think it was nice of the maker of this meme to save the most ridiculous claim for last. Sundials work on a globe. In fact, it is because the Earth is a sphere that different sundial designs are used at different latitudes. Furthermore, here is a video on how a crude sundial can be used to determine the shape of the Earth:
Strike four. Getting four strikes at a single at-bat means you should just give up the game altogether.