It looks like the information you are looking for is store in the "index.php" file that gets downloaded when the web page loads.
The current link for Maine is "https://gasprices.aaa.com/index.php?premiumhtml5map_js_data=true&map_id=21&r=89346&ver=5.9.3".
I am not sure what the r=89346 value is for, maybe a timestamp, tracking id, temporary token (to prevent web scraping) etc. I suspect this URL will change thus you may need to use the developer tools on the browser to obtain the current url.
Also, map_id refers to state but I don't know the rational, Florida is 1, NC is 35 and Maine is 21.
Download this file, then extract the JSON data and convert.
library(dplyr)
#read the index_php file and turn it into character string
index_php <-readLines("https://gasprices.aaa.com/index.php?premiumhtml5map_js_data=true&map_id=21&r=19770&ver=5.9.3")
index_php <- paste(index_php, collapse = " ")
#extract out the correct JSON data part and convert
jsondata <- stringr::str_extract(index_php, "\\{\"st1\":.+?\\}\\}")
data<-jsonlite::fromJSON(jsondata)
#create a data frame with the results
answer <- bind_rows(data)
id name shortname link comment image color_map color_map_over
<int> <chr> <chr> <chr> <chr> <chr> <chr> <chr>
1 1 Androscoggin "" "" $4.964 "" #ca3338 #ca3338
2 2 Aroostook "" "" $4.928 "" #dd7a7a #dd7a7a
3 3 Cumberland "" "" $4.944 "" #ca3338 #ca3338
4 4 Franklin "" "" $4.936 "" #dd7a7a #dd7a7a
5 5 Hancock "" "" $4.900 "" #01b5da #01b5da
6 6 Kennebec "" "" $4.955 "" #ca3338 #ca3338
有一些额外的专栏需要删除，我留给读者作为练习.