Distance and voltage/watt loss?
Preamble:

I think what you're missing is a fundamental understanding of voltage, current, resistance, and power. I encourage you to do some research to get these concepts down.

There are countless posts here on these topics:


What exactly is voltage?
What is an amp (and other such basic questions) in the simplest possible terms?
I do not understand what power actually is
Understanding electrical consumption




Your Scenario Explained:

Okay, so here are my thoughts to help answer your question:

Simple surge protectors are basically a splitter with some MOVs to arrest high voltage transients (spikes), a circuit breaker, and other components. For the purposes of your question, they are basically serving as an extension cord and adding a plug/socket connection (and a point of failure).

The length of wire that you operate a device is sort of useless information without also knowing the wire gauge (thickness of wire). Most residential surge protectors and extension cords are going to have somewhere between 18 and 12 gauge wire. You can think of wire as a low value resistor, which means it's going to imperfectly transfer power from point A to point B. Any time you have resistance, you have power loss which in this case is unwanted heat.

18 AWG (American wire gauge) is thinner than 16 AWG. 16 AWG is thinner than 14 AWG, and so on. The thinner the wire, the more resistance it has.

Let's pretend that everything you're using is 18 AWG. Connections (socket to plug) can have inherent added resistance because of corrosion, contamination, loose fit resulting in limited surface area making a connection, and so forth. Let's ignore those for the moment as well.

You have, as best I can tell:


TV (8 ft cord), plugged into
an extension cord (10 ft), plugged into
a surge protector (6 ft), plugged into
another surge protector (10 ft)


The total length of this arrangement is 34 feet. Electricity requires a full loop (circuit), so you have to double this length to determine how much extra wire resistance you're adding with this setup.

You can find tables online which provide resistance of wire per unit length, such as this one. 68 feet of 18 AWG wire adds 0.434 ohms.

I'm not sure from how you phrased it, but I'll assume your TV consumes 110 watts. That sounds about right for a modern flat screen TV of about 40-60 inches. I'll further assume that you're in the USA where mains electrical is 120 volts.

Ohm's Law is something you should study in the course of learning about voltage, current, resistance, and power.

The TV presumably operates on 120V AC and consumes 110W. (Note that the TV consumes power, while the surge protectors specify a maximum allowed power. They don't consume it, they just allow up to that threshold. This point may be the most important one with regard to your confusion.) With some basic math, this works out to about 0.92 amperes of current. (Keep in mind this should be the "maximum" or "worst case" since that's what appliance ratings are meant to convey.)  That much current would also flow through the extension cords and whatnot, so you can now calculate how much power is lost to the wire: \$P = 0.92^2 A \times 0.434 Ω = 0.367 W\$. Basically, not even half a watt.

Spread out through the length of the wire, the temperature increase is negligible. In short, there's no problem with the length of wire you're using... given the load you're powering.

If you decided instead to plug a table saw into this, you'd probably trip the breaker on one of the surge protectors. That's because a table saw (or a multitude of power-hungry devices) will require much more than 110 watts.



Understanding the Specs:

The surge protector ratings you're looking at are the specifications as to what their maximum load is.

Take the first spec you provided, for example:

15A 125V 1875W

15A: This means that no more than 15 amperes of current should be drawn from the protector. Why? Because the manufacturer (hopefully) selected components that are safe up to that amount. More than that, and the circuit breaker should trip. The circuit breaker's job is to stop the surge protector from supplying more current than its components are rated for. And to protect you from failures that could result in fire.

125V: This means the breaker is designed to operate at no more than 125 volts (RMS AC, but that's beyond the scope of this answer). If you try to plug it into a foreign mains outlet that uses 240V, all of the specifications are invalid because you're not using it as intended/designed.

1875W: This is a sort of redundant specification. Power is equal to voltage times current. 125 volts times 15 amperes equals 1875 watts. In theory the label need only show power and voltage (or current and voltage).



Conclusion:


  Does the voltage/watt loss for that much cable length affect the amount of power this TV will receive that it will not be able to have the required power it needs?


Yes, it affects how much power the TV consumes (by way of dropping the voltage that the TV "sees"). You're on the right track to be concerned about this. In this case, since the TV power requirement is relatively low, and the added wire length (resistance) is not terribly high, you should be just fine.

Increasing the load (things that require more power), increasing the length of wire feeding the load, or decreasing the wire gauge: all can contribute to a situation where the load is inadequately supplied and may cause failure.