The thick gel-coat on the faux teak has a hard life with the combination of UV and temperature cycling. It's great non slip but it's too much to expect it to last forever. If the deck is very old then the likely option is to reluctantly sand down the teak texture. You then need to replace with a different non-skid texture. Any smooth bit of deck would be very dangerous when wet. The look will be different to original but safety comes first. The normal painted no-slip method would be using matt finish 2 pack poly paint and sprinkle evenly with fine glass beads whilst wet, then give a second coat once that has dried to cover the beads. Different size beads are available depending upon what look you want and whether the use is for shoe wearers or bare feet.
If you really want to keep the stripes this could be done but a lot of work. Basically it would be as Bill describes but with the use of glass beads on the boards.
A different method I've used before is to paint a deck with a generous coat of 2 pack paint then when wet sprinkle with sugar. Allow to dry then rinse off the sugar which will leave a texture in the paint with no extra ingredient. Non slip paints that have the non-slip ingredient mixed in are, in my experience, hard to get to look even.
If you have just a small area of cracked or damaged faux teak, another method is to use a good part of deck to make a texture-mould out of latex then use this on the repair to recreate the original non-slip pattern. This is effective on other pattern non-slip deck gelcoat too. Colour matching is very difficult though.
John, Popeye, Maramu #91