The Mig29k has 38 percent more internal fuel than its predecessor, but is also heavier. Sure they have videos of taking off from their ski jumps with a centerline tank and 2 missiles, but that is most likely with downloaded fuel loadouts internally - just google it, or look through the various defense sites, but those wiki range quotes are ridiculous for a Mig29k on that short take off jump roll.
1st of all MiG-29K isn't the MiG-29 of 80th-90th - the fuel payload was increased as you mentioned, engines improved...
Also I don't see any reason to carry central line tank if you can carry fuel internally.
I assume that there are some "manipulations" as always done (like F-35A's range that has "better range" than F-16) also
F-18 combat radius I found were with bombs etc.
See... I clearly agree that it has no F-16's range with 3xDT+2xCFT... but its range isn't poor.
If MiG-29K can takeoff from skijump with full internal fuel and center line tank and can carry some useful weapons - it would have good range.
According to the videos it is a normal practice.
But I still think that its range way better than any STOVL aircraft like Harrier or F-35B - because it is just a conventional aircraft with very minimal overhead over shore based one (for example STOBAR aircraft shouldn't withstand the forces of catapult that BTW much stronger than that of arresting hook).
I think many western defense analytic clearly underestimate the capability of STOBAR or don't understand how it works...
Once plane takes off from skijump it has vertical speed and continues to accelerate horizontally decelerating vertically "falling" it significantly extends the length of the "runway" such that efficiently it works very well. Also it starts to accelerate when the engines work at 100% and only than the barrier released not wasting time on "partial thrust" acceleration.
Let's do some calculations to explain that ski-jump actually works exceptionally well...
Loaded MiG-29K weights 18,550kg (internal fuel).
Maximal takeoff weight is 24,500kg
Thrust is 2x9,000 kgf... giving 0.73 thrust to weight ratio at full load.
Vikramaditya has 180m runway length giving:
Initial takeoff run of ~7s and inital speed ~51m/s = ~100knots
Given takeoff ramp of 14 deg, we get initial vertical speed of 12.3 m/s and horisontal speed of ~95knots relatively to the ship.
Lets assume the ship has 20knots of speed, so wind speed under the wings is around 115knots...
Now takeoff speed of normally loaded MiG-29 is around 280km/h (cound't find better reference) so assuming that at 280km/h ~= 150 knots wings can hold loaded weight than at maximal takeoff weight the required ~ 173 knots... (lift proportional to square of speed)
Now we have plane with 12.3 ms vertical speed with unloaded wings having (115/173)^2 =45% of required lift accelerating...
Small calculations show how the progress go
The table includes: time from takeoff, horizontal speed, the G pilot feels and the distance the plane traveled relatively to the ship...
Time 7.1 s, hspeed=116.1 knots, vspeed= 12.3 m/s G=0.45 flew=180.0 m
Time 7.2 s, hspeed=117.5 knots, vspeed= 11.8 m/s G=0.46 flew=185.0 m
Time 7.3 s, hspeed=118.9 knots, vspeed= 11.2 m/s G=0.47 flew=190.0 m
Time 7.4 s, hspeed=120.3 knots, vspeed= 10.7 m/s G=0.48 flew=195.1 m
Time 7.5 s, hspeed=121.7 knots, vspeed= 10.2 m/s G=0.49 flew=200.3 m
Time 7.6 s, hspeed=123.1 knots, vspeed= 9.7 m/s G=0.50 flew=205.6 m
Time 7.7 s, hspeed=124.5 knots, vspeed= 9.2 m/s G=0.51 flew=210.9 m
Time 7.8 s, hspeed=125.9 knots, vspeed= 8.8 m/s G=0.52 flew=216.3 m
Time 7.9 s, hspeed=127.3 knots, vspeed= 8.3 m/s G=0.54 flew=221.8 m
Time 8.0 s, hspeed=128.7 knots, vspeed= 7.9 m/s G=0.55 flew=227.4 m
Time 8.1 s, hspeed=130.1 knots, vspeed= 7.4 m/s G=0.56 flew=233.0 m
Time 8.2 s, hspeed=131.5 knots, vspeed= 7.0 m/s G=0.57 flew=238.7 m
Time 8.3 s, hspeed=132.9 knots, vspeed= 6.6 m/s G=0.58 flew=244.5 m
Time 8.4 s, hspeed=134.3 knots, vspeed= 6.2 m/s G=0.60 flew=250.3 m
Time 8.5 s, hspeed=135.7 knots, vspeed= 5.8 m/s G=0.61 flew=256.2 m
Time 8.6 s, hspeed=137.1 knots, vspeed= 5.4 m/s G=0.62 flew=262.2 m
Time 8.7 s, hspeed=138.5 knots, vspeed= 5.1 m/s G=0.63 flew=268.3 m
Time 8.8 s, hspeed=139.9 knots, vspeed= 4.7 m/s G=0.65 flew=274.4 m
Time 8.9 s, hspeed=141.3 knots, vspeed= 4.4 m/s G=0.66 flew=280.6 m
Time 9.0 s, hspeed=142.7 knots, vspeed= 4.0 m/s G=0.67 flew=286.9 m
Time 9.1 s, hspeed=144.1 knots, vspeed= 3.7 m/s G=0.69 flew=293.2 m
Time 9.2 s, hspeed=145.5 knots, vspeed= 3.4 m/s G=0.70 flew=299.6 m
Time 9.3 s, hspeed=146.9 knots, vspeed= 3.1 m/s G=0.71 flew=306.1 m
Time 9.4 s, hspeed=148.3 knots, vspeed= 2.9 m/s G=0.73 flew=312.7 m
Time 9.5 s, hspeed=149.7 knots, vspeed= 2.6 m/s G=0.74 flew=319.3 m
Time 9.6 s, hspeed=151.1 knots, vspeed= 2.4 m/s G=0.76 flew=326.0 m
Time 9.7 s, hspeed=152.5 knots, vspeed= 2.1 m/s G=0.77 flew=332.8 m
Time 9.8 s, hspeed=153.9 knots, vspeed= 1.9 m/s G=0.78 flew=339.6 m
Time 9.9 s, hspeed=155.3 knots, vspeed= 1.7 m/s G=0.80 flew=346.6 m
Time 10.0 s, hspeed=156.8 knots, vspeed= 1.5 m/s G=0.81 flew=353.5 m
Time 10.1 s, hspeed=158.2 knots, vspeed= 1.3 m/s G=0.83 flew=360.6 m
Time 10.2 s, hspeed=159.6 knots, vspeed= 1.2 m/s G=0.84 flew=367.8 m
Time 10.3 s, hspeed=161.0 knots, vspeed= 1.0 m/s G=0.86 flew=375.0 m
Time 10.4 s, hspeed=162.4 knots, vspeed= 0.9 m/s G=0.87 flew=382.2 m
Time 10.5 s, hspeed=163.8 knots, vspeed= 0.8 m/s G=0.89 flew=389.6 m
Time 10.6 s, hspeed=165.2 knots, vspeed= 0.7 m/s G=0.90 flew=397.0 m
Time 10.7 s, hspeed=166.6 knots, vspeed= 0.6 m/s G=0.92 flew=404.5 m
Time 10.8 s, hspeed=168.0 knots, vspeed= 0.5 m/s G=0.93 flew=412.1 m
Time 10.9 s, hspeed=169.4 knots, vspeed= 0.4 m/s G=0.95 flew=419.7 m
Time 11.0 s, hspeed=170.8 knots, vspeed= 0.4 m/s G=0.96 flew=427.4 m
Time 11.1 s, hspeed=172.2 knots, vspeed= 0.4 m/s G=0.98 flew=435.2 m
Time 11.2 s, hspeed=173.9 knots, vspeed= 0.4 m/s G=1.00 flew=445.0 m
Edit: improved calculation resolution.
You can see that once the plane reaches required speed it had flown around 450m and still has some vertical speed to spare at Maximal takeoff weight.
Now the takeoff speed I took is for ordinary MiG-29, MiG-29K has lower stall speed and probably has better numbers.
So I hope now it is more clear how ski-jump works - the "actual" runway becomes much longer than it looks like but when you look at the numbers... they are pretty good ones.