Treriksröset is not reachable by road. You can get there on foot or ski (perhaps kayak too but there may be some rapids to navigate upstream). Mountain-bike may work (I'm not sure). From your screenshot it appears Google Maps knows the trail on the Norwegian side, but not the shorter and much more popular hiking trail on the Finnish side. Openstreetmap has all trails (including some not on any other maps; be careful assuming anything about those). You can explore the Finnish topographic map online via retkikartta.fi, paper maps are for sale in Kilpisjärvi. If you want to hike on the Norwegian side via Goldahytta, try norgeskart. For maps on the Swedish side, try Swedish fjällkartan (mountain map). I believe the Swedish fjällkartan will be for sale in Kilpisjärvi but I'm less sure about the Norwegian maps.
Gerald Schneider pointed out you can get there by dogsled. That works, but only in winter. In summer and autumn (June to September) you can get to within 3 km by boat. The last 3 km from Golddaluokta are still on foot. The trail is shown on Swedish fjällkartan and on Openstreetmap.
Your options in the snow-free season:
- Boat from Kilpisjärvi to Goldaluokta/Koltaluokta (Sweden) + 3 km hike each way. June to September. See mallalaiva for details on the boat. I believe the hiking trail is easy but it is a hiking trail through a rather wild area, not a stroll in the park, so you do need some outdoor preparation. It can be cold, wet, and windy any time of year (wet is unlikely in winter) and you can't immediately run for shelter (although there does appear to be a wilderness cabin on the Finnish side near Treriksröset, it's not staffed and I don't know if it's normally locked or open).
Hiking trail Goldaluokta–Treriksröset. Source: Skogsfrun, Wikimedia Commons, CC-BY-SA 3.0.
- Hike from Kilpisjärvi (Finland). 11 km each way. This is part of the long distance Nordkalottruta/Kalottireiti hiking trail. I've done this and found it easy, but I'm an experienced hiker. It was busy in September; we met 10× more people on those 11 km than in the 150 km prior.
- Hike from Gálggojávri (Norway) via Goldahytta. 13 km to Goldahytta (where you can sleep), then another 3 km to Treriksröset. That appears to be the trail shown on your Google Map screenshot (including some roadwalking on E8). Some WW II artefacts along the way. Description (in Norwegian) with photos at kugo.no. This is certainly the toughest alternative and not recommended if you're not experienced with wilderness hiking and navigation. I certainly would not attempt a round trip in a day. Walking times as reported by Google Maps, Openstreetmap, or others are completely useless for wilderness/mountain trails/routes as you may have to ford rivers, scramble through boulder fields, and navigate through the fog.
You may be able to do it on a mountainbike; I don't remember how easy the trails from Goldahytta or Kilpisjärvi are and I haven't done the others. There are other routes but they will be much longer (certainly more than a day).
When there is snow, you can go on skis, by dog-sled, or by snowmobile. You can even rent a fat bike and try to get there by bicycle.
If you plan an outdoorsy way of getting there you may want to consult The Great Outdoors Stack Exchange.
Incidentally, I would recommend to avoid going there between mid-June and mid-August as the mosquitoes in that area are quite vicious. Autumn (late August to mid September) is the best time of the year (and rather popular in Finland).