This is a similar route that is in Paddy Dillon's book on Tenerife. His route is 32km with 2,300m (Asc:) and 2,100 (Desc: -approx). On the distance, this is different as the start was from Boca Tauce because of a car 'malfunction'. The normal starting point is the Parador Hotel in the Parque Nacional del Teide. The actual Asc:/Desc: are 2,500m/2,300m on this route. The '5702m' and '5034m' that the file is quoting are definitely not correct, trust me.
You'll need two cars or arrange for drop-off and pick-up. I can't see any way of doing this by relying on the bus service up around Teide. There are no taxi's based in the area so if you need to call one, it would have to come up from Vilaflor. The cost of a taxi from Parque Nacional del Teide to the South of the island is about €50 but the spin is about one hour.
The route is pretty well marked with a series of 'Sendero' numbers. The only place that it was difficult to pick up a track was 'Sendero 23' just beyond Roques de Garcia. It's much easier to walk on the specified tracks. In hindsight, it's pretty defined on the map above but I wasn't relying on openstreet on the day.
You'll need a permit to climb the 163m from the cable car station to the summit of Teide (3,717.98m) - Route No. 10 (Telesforo Bravo) - https://www.reservasparquesnacionales.es/real/ParquesNac/usu/html/Previo-inicio-reserva-oapn.aspx?ii=6ENG&cen=2&act=%201
If there's no snow/ice on Teide, it's a great walk.
Walk finish is Montana Blanca car park.