How can I make it so a player gets 1 point every second when walking?

You can use the Humanoid.MoveDirection property to determine if the Humanoid is in motion or not.

Humanoid.MoveDirection is a Vector3 that contains data regarding the direction that the humanoid is moving in. Likewise if the Humanoid is not moving at all, it will be 0, 0, 0, therefore you simply need to check if the Humanoid's MoveDirection is not equal to Vector3.new(0, 0, 0) to determine whether or not you should add a point for the elapsed second.

-Here is a basic setup:

lcoal amount = 1;
local points = "Steps";
local wte = wait;
local vec3 = Vector3;

local function CheckForWalk(plr, hum)
    pcall(function()
        while wte() do
            if hum.MoveDirection ~= vec3.new(0, 0, 0) then --if the character is moving
                while wte(1) do --while the player is moving, increase their step points each second.
                    if hum.MoveDirection ~= vec3.new(0, 0, 0) then
                        plr.leaderstats[points].Value = plr.leaderstats[points].Value + amount;
                    else
                        break;
                    end
                end
            end
        end
    end);
end

game.Players.PlayerAdded:connect(function(plr)
    repeat
        wte();
    until plr.Character;
    local hum = plr.Character:WaitForChild("Humanoid");
    CheckForWalk(plr, hum);
    plr.Changed:connect(function(prop) --we need to re-call the CheckForWalk function when the player dies, because the old one would have halted execution if the old humanoid dies.
        if prop == "Character" then --make sure that the Character is a different model than before
            repeat wte() until plr.Character;
            local hum = plr.Character:WaitForChild("Humanoid");
            CheckForWalk(plr, hum);
        end
    end);
end);

I hope this helps.

I tried it out myself. I noticed the the Running event for Humanoid will fire multiple times even if you just move once, that's the cause of it giving multiple points at once. To fix that, I made a debounce for the script. I also noticed that with your method, speed is a constant and will forever add points once you get into motion once, so I used c.Torso.Velocity.magnitude instead. Here's the final script I got working for myself:

game.Players.PlayerAdded:connect(function(plr)
    plr.CharacterAdded:connect(function(char)
        local running = false
        char:WaitForChild("Humanoid").Running:connect(function()
            if running == false then
                running = true
                while char.Torso.Velocity.magnitude > 0 do
                    wait(1)
                    plr:WaitForChild("leaderstats").points.Value = plr.leaderstats.points.Value + 1
                    print(char.Torso.Velocity.magnitude)
                end
                running = false
            end
        end)
    end)
end)

You can make a loop where it checks if MoveDirection (A property in Humanoids) is not Vector3.new(0,0,0) (Standing Still) and give the player points based on that

local plr = game.Players.LocalPlayer
local char = workspace:WaitForChild(plr.Name)
local Humanoid = char:WaitForChild("Humanoid")
while true do
    if Humanoid.MoveDirection ~= Vector3.new(0,0,0) then
        print("Walking")
        plr:WaitForChild("leaderstats").points.Value = plr.leaderstats.points.Value + 1
    else
        print("Standing")
    end
    wait(1)
end