Traefik does not work with .me domains

Something else is up with your configuration. Posting all of your configuration will help.

It is possible your http://viceartur is also returning the 404. Access log can help determine this(treafik_router_name is present if matched to a router), I like to use json format for this as lots of useful information is included by default.

Yes, .me domains do work.

docker-compose.yaml
version: "3.8"

services:
  traefik:
    image: "traefik:v2.5"
    command:
    - --entrypoints.web.address=:80
#    - --entrypoints.web.http.redirections.entrypoint.to=websecure
#    - --entrypoints.web.http.redirections.entrypoint.permanent=true
    - --entrypoints.websecure.address=:443
    - --entrypoints.websecure.http.tls=true
    - --providers.docker=true
    - --providers.docker.exposedbydefault=false
    - --accesslog
    - --accesslog.format=json
    - --api
    - --log.level=INFO
    - --log.format=json
    labels:
      traefik.enable: "true"
      traefik.http.routers.api.rule: Host(`traefik.localhost`)
      traefik.http.routers.api.service: api@internal
      traefik.http.services.dummy.loadBalancer.server.port: 65535
      traefik.http.routers.api.entrypoints: websecure

    ports:
      - published: 80
        target: 80
      - published: 443
        target: 443
    volumes:
      - "/var/run/docker.sock:/var/run/docker.sock:ro"
  whoami:
    image: traefik/whoami
    labels:
      traefik.enable: "true"
      traefik.http.routers.w.rule: Host(`example.com`) || Host (`example.me`)
curl example.com
curl --resolve example.com:80:127.0.0.1 --resolve example.me:80:127.0.0.1 http://example.com
Hostname: 087957d0c991
IP: 127.0.0.1
IP: 172.27.0.3
RemoteAddr: 172.27.0.2:36850
GET / HTTP/1.1
Host: example.com
User-Agent: curl/7.68.0
Accept: */*
Accept-Encoding: gzip
X-Forwarded-For: 172.27.0.1
X-Forwarded-Host: example.com
X-Forwarded-Port: 80
X-Forwarded-Proto: http
X-Forwarded-Server: 5f69047612bf
X-Real-Ip: 172.27.0.1
curl example.me
curl --resolve example.com:80:127.0.0.1 --resolve example.me:80:127.0.0.1 http://example.me
Hostname: 087957d0c991
IP: 127.0.0.1
IP: 172.27.0.3
RemoteAddr: 172.27.0.2:36850
GET / HTTP/1.1
Host: example.me
User-Agent: curl/7.68.0
Accept: */*
Accept-Encoding: gzip
X-Forwarded-For: 172.27.0.1
X-Forwarded-Host: example.me
X-Forwarded-Port: 80
X-Forwarded-Proto: http
X-Forwarded-Server: 5f69047612bf
X-Real-Ip: 172.27.0.1