Edit after Question Update:
This is the abc csv:
1,name,ABC,GHI,DEF,JKL
2,name,GHI,DEF,ABC,
3,name,JKL,GHI,ABC,DEF
This is the company csv (it is necessary to watch the commas carefully):
1,name,1012B-Amazon,2044C-Flipcart,Bosh27-Walmart
2,name,Kelvi20-Flipcart,LG-Walmart,
3,name,Kenstar-Walmart,Sony-Amazon,Kenstar-Flipcart
4,name,LG18-Walmart,Bravia-Amazon,
Here is the code
import pandas as pd
import numpy as np
#These solution assume that each value that is not empty is not repeated
#within each row. If that is not the case for your data, it would be possible
#to do some transformations that the non empty values are unique for each row.    
#"get_company" returns the company if the value is non-empty and an
#empty value if the value was empty to begin with:
def get_company(company_item):
    if pd.isnull(company_item):
        return np.nan
    else:
        company=company_item.split('-')[-1]
        return company
#Using the "define_sort_order" function, one can retrieve a template to later
#sort all rows in the sort_abc_rows function. The template is derived from all
#values, aside from empty values, within the matrix when "by_largest_row" = False.
#One could also choose the single largest row to serve as the
#template for all other rows to follow. Both options work similarly when
#all rows are subsets of the largest row i.e. Every element in every
#other row (subset) can be found in the largest row (or set)
#The difference relates to, when the items contain unique elements,
#Whether one wants to create a table with all sorted elements serving
#as the columns, or whether one wants to simply exclude elements
#that are not in the largest row when at least one non-subset row does not exist 
#Rather than only having the application of returning the original data rows,
#one can get back a novel template with different values from that of the
#original dataset if one uses a function to operate on the template
def define_sort_order(data,by_largest_row = False,value_filtering_function = None):
    if not by_largest_row: 
        if value_filtering_function:
            data = data.applymap(value_filtering_function)
        #data.values returns a numpy array                 
        #with rows and columns. .flatten()
        #puts all elements in a 1 dim array
        #set gets all unique values in the array
        filtered_values = list(set((data.values.flatten())))
        filtered_values = [data_value for data_value in filtered_values if not_empty(data_value)]
        #sorted returns a list, even with np.arrays as inputs
        model_row = sorted(filtered_values)
    else:
        if value_filtering_function:
            data = data.applymap(value_filtering_function)
        row_lengths = data.apply(lambda data_row: data_row.notnull().sum(),axis = 1)
        #locates the numerical index for the row with the most non-empty elements:
        model_row_idx = row_lengths.idxmax()
    #sort and filter the row with the most values:
        filtered_values = list(set(data.iloc[model_row_idx]))
        model_row = [data_value for data_value in sorted(filtered_values) if not_empty(data_value)] 
    return model_row
#"not_empty" is used in the above function in order to filter list models that
#they no empty elements remain
def not_empty(value):
    return pd.notnull(value) and value not in ['','  ',None]
#Sorts all element in each _row within their corresponding position within the model row.
#elements in the model row that are missing from the current data_row are replaced with np.nan
def reorder_data_rows(data_row,model_row,check_by_function=None):
    #Here, we just apply the same function that we used to find the sorting order that
    #we computed when we originally #when we were actually finding the ordering of the model_row.
    #We actually transform the values of the data row temporarily to determine whether the
    #transformed value is in the model row. If so, we determine where, and order #the function
    #below in such a way.
    if check_by_function: 
        sorted_data_row = [np.nan]*len(model_row) #creating an empty vector that is the
                          #same length as the template, or model_row
        data_row = [value for value in data_row.values if not_empty(value)]
        for value in data_row:
            value_lookup = check_by_function(value)
            if value_lookup in model_row:
                idx = model_row.index(value_lookup)
                #placing company items in their respective row positions as indicated by
        #the model_row                #
                sorted_data_row[idx] = value    
    else:
        sorted_data_row = [value if value in data_row.values else np.nan for value in model_row]
    return pd.Series(sorted_data_row)
##################### ABC ######################
#Reading the data:
#the file will automatically include the header as the first row if this the  
#header = None option is not included. Note: "name" and the 1,2,3 columns are not in the index.
abc = pd.read_csv("abc.csv",header = None,index_col = None)
# Returns a sorted, non-empty list. IF you hard code the order you want,
# then you can simply put the hard coded order in the second input in model_row and avoid
# all functions aside from sort_abc_rows.
model_row = define_sort_order(abc.iloc[:,2:],False)
#applying the "define_sort_order" function we created earlier to each row before saving back into
#the original dataframe
#lambda allows us to create our own function without giving it a name.
#it is useful in this circumstance in order to use two inputs for sort_abc_rows
abc.iloc[:,2:] = abc.iloc[:,2:].apply(lambda abc_row: reorder_data_rows(abc_row,model_row),axis = 1).values
#Saving to a new csv that won't include the pandas created indices (0,1,2)
#or columns names (0,1,2,3,4):
abc.to_csv("sorted_abc.csv",header = False,index = False)
################################################
################## COMPANY #####################
company = pd.read_csv("company.csv",header=None,index_col=None)
model_row = define_sort_order(company.iloc[:,2:],by_largest_row = False,value_filtering_function=get_company)
#the only thing that changes here is that we tell the sort function what specific
#criteria to use to reorder each row by. We're using the result from the
#get_company function to do so. The custom function get_company, takes an input
#such as Kenstar-Walmart, and outputs Walmart (what's after the "-").
#we would then sort by the resulting list of companies. 
#Because we used the define_sort_order function to retrieve companies rather than company items in order,
#We need to use the same function to reorder each element in the DataFrame
company.iloc[:,2:] = company.iloc[:,2:].apply(lambda companies_row: reorder_data_rows(companies_row,model_row,check_by_function=get_company),axis=1).values
company.to_csv("sorted_company.csv",header = False,index = False)
#################################################
Here is the first result from sorted_abc.csv:
1  name  ABC  DEF  GHI  JKL
2  name  ABC  DEF  GHI  NaN
3  name  ABC  DEF  GHI  JKL
After modifying the code to the subsequent form inquired about,
here is the  sorted_company.csv that resulted from running the
script.
1  name    1012B-Amazon    2044C-Flipcart   Bosh27-Walmart
2  name             NaN  Kelvi20-Flipcart       LG-Walmart
3  name     Sony-Amazon  Kenstar-Flipcart  Kenstar-Walmart
4  name   Bravia-Amazon               NaN     LG18-Walmart
I hope it helps!