Using dplyr and tidyr, reshape the data from wide to long, then group by count.
library(dplyr)
library(tidyr)
gather(df1, key = author, value = name, -venue) %>% 
  select(venue, name) %>% 
  group_by(venue) %>% 
  summarise(n = n_distinct(name, na.rm = TRUE))
# # A tibble: 3 × 2
#   venue     n
#   <chr> <int>
# 1     A     2
# 2     B     5
# 3     C     2
data
df1 <- read.table(text ="
venue,author0,author1,author2
A,John,Mary,NA
B,Peter,Jacob,Isabella
C,Lia,NA,NA
B,Jacob,Lara,John
C,Mary,NA,NA
B,Isabella,NA,NA
", header = TRUE, sep = ",", stringsAsFactors = FALSE)
Edit: Saved your Excel sheet as CSV, then read in using read.csv, then above code returns below output:
df1 <- read.csv("Journal_Conferences_Authors.csv", na.strings = "#N/A")
# output
# # A tibble: 427 × 2
#                                     venue     n
#                                    <fctr> <int>
# 1                                    AAAI     4
# 2                                     ACC     4
# 3                               ACIS-ICIS     5
# 4  ACM SIGSOFT Software Engineering Notes     1
# 5       ACM Southeast Regional Conference     5
# 6                                ACM TIST     3
# 7       ACM Trans. Comput.-Hum. Interact.     3
# 8                                    ACML     2
# 9                                    ADMA     2
# 10             Advanced Visual Interfaces     3
# # ... with 417 more rows