The Wikipedia list you link to specifies human rated lunar rockets; that's a very short list, because it requires, at minimum, lunar landing and safe return of a multi-ton spacecraft.
For a one-way, 1000 kg lander, many more rockets are capable of the job; any launcher that can get at least 8-10 tons to LEO* could soft-land 1 ton on the lunar surface with an appropriate transfer stage/spacecraft/lander design. That includes, among other designs:
- Falcon 9
- Atlas V
- Delta IV
- Proton
- Long March 5
- Ariane 5
- GSLV Mk III
And possibly Soyuz or Antares.
New Glenn would certainly be able to if it's built; I believe the current Firefly, Vector, and Rocket Lab designs are all too small.
* Assume the transfer and lander stages are using hypergolic fuels with ~3000 m/s exhaust velocity (~305 s Isp). Take a conservative delta-v budget of 3300 m/s for translunar injection orbit, 700 m/s for lunar orbital insertion, 2200 m/s for descent and landing = 6200 m/s. Apply rocket equation:
$$ 6200 = 3000 \ln \frac {m_0} {m_f} $$
Hit it with the algebra stick...
$$ 2.067 = \ln \frac {m_0} {m_f} $$
Thus...
$$ \frac {m_0} {m_f} = e ^ {2.067} = 7.898 $$
Thus the initial (fully fueled) mass could be around 8 times the final (landed) mass.