The basic results, including how large the risk increase is, are in the abstract at your link:

Results The most common anticholinergic classes used were tricyclic antidepressants, first-generation antihistamines, and bladder antimuscarinics. During a mean follow-up of 7.3 years, 797 participants (23.2%) developed dementia (637 of these [79.9%] developed Alzheimer disease). A 10-year cumulative dose-response relationship was observed for dementia and Alzheimer disease (test for trend, P < .001). For dementia, adjusted hazard ratios for cumulative anticholinergic use compared with nonuse were 0.92 (95% CI, 0.74-1.16) for TSDDs of 1 to 90; 1.19 (95% CI, 0.94-1.51) for TSDDs of 91 to 365; 1.23 (95% CI, 0.94-1.62) for TSDDs of 366 to 1095; and 1.54 (95% CI, 1.21-1.96) for TSDDs greater than 1095. A similar pattern of results was noted for Alzheimer disease. Results were robust in secondary, sensitivity, and post hoc analyses.

(TSDD is total standardized daily doses)